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United States Patent |
6,101,272
|
Noguchi
|
August 8, 2000
|
Color transforming method
Abstract
The improved color transformation method comprises determining for each
pixel a lightness component specified between a maximum and a minimum
value for three signals and chromaticity components obtained by excluding
the lightness component from the three signals, amplifying or attenuating
the thus obtained chromaticity components in accordance with the three
signals and adding them to the lightness component amplified or attenuated
in accordance with the three signals. Even if the input original image is
a subject, a transmission original hardcopy image, a reflection original
softcopy image or an original softcopy image, one can create a reproduced
hardcopy image such as a reflective print which is extremely faithful to
the input original image or, alternatively, one can provide a monitor
display of a reproduced image (a reproduced soft copy image) which is also
extremely faithful to the input original image. The processing system is
very simple and permits realtime execution. Even transmission original
hardcopy images and original softcopy images which are upset in either
color balance or density balance or both can be effectively processed to
yield reproduced reflection hardcopy image or reproduced softcopy images
which feature good balances.
Inventors:
|
Noguchi; Takafumi (Kanagawa, JP)
|
Assignee:
|
Fuji Photo Film Co., Ltd. (Kanagawa, JP)
|
Appl. No.:
|
990006 |
Filed:
|
December 12, 1997 |
Foreign Application Priority Data
| Dec 12, 1996[JP] | 8-332037 |
| Dec 12, 1996[JP] | 8-332043 |
| May 28, 1997[JP] | 9-138853 |
Current U.S. Class: |
382/167; 358/520 |
Intern'l Class: |
G06K 009/00; G03F 003/08 |
Field of Search: |
358/520,518,523,524,539,1.9
382/162,165,167,166
348/606,631,653,662,663,713
|
References Cited
U.S. Patent Documents
4839718 | Jun., 1989 | Hemsky et al. | 358/520.
|
4963925 | Oct., 1990 | Miyazaki | 355/77.
|
5060060 | Oct., 1991 | Udagawa | 358/520.
|
5317426 | May., 1994 | Hoshino | 358/515.
|
5363218 | Nov., 1994 | Hoshino | 358/518.
|
5384601 | Jan., 1995 | Yamashita et al. | 358/520.
|
5450216 | Sep., 1995 | Kasson | 382/167.
|
5488670 | Jan., 1996 | Suzuki et al. | 382/165.
|
5502579 | Mar., 1996 | Kita et al. | 358/518.
|
Primary Examiner: Nguyen; Madeleine
Attorney, Agent or Firm: Sughrue, Mion, Zinn, Macpeak & Seas, PLLC
Claims
What is claimed is:
1. A color transformation method, in which input image data from an image
input device, represented by three signals that are mutually independent
and provide a color of gray when values of the three signals coincide, are
subjected to a color transformation to produce output image data for
production of an image by an image output device, the output image data
being represented by three color transformed signals, which method
comprises the steps of:
determining, for each pixel:
a lightness component specified between a maximum value and a minimum value
for said three signals, and
three chromaticity components obtained by subtracting said lightness
component from said three signals respectively;
modifying the three chromaticity components in accordance with said three
signals, said modifying being one of amplifying and attenuating; and
adding the chromaticity components to said lightness component modified in
accordance with said three signals to produce said output image data.
2. The color transforming method according to claim 1, wherein, when said
three signals are designated by (B,G,R) and said three color transformed
signals by (B',G',R') for each pixel, the color transformation from said
three signals to said three color transformed signals is represented by:
B'=K.sub.01 {B-f(B,G,R)}+k.sub.1 {f(B,G,R)-C.sub.1 }+C.sub.2
G'=K.sub.02 (G-f(B,G,R)}+k.sub.1 {f(B,C,R)-C.sub.1 }+C.sub.2
R'=K.sub.03 {R-f(B,G,R)}+k.sub.1 (f(B,G,R)-C.sub.1 }+C.sub.2
where;
f(B,G,R) is a function that satisfies min(B,G,R).ltoreq.f(B,G,R).ltoreq.max
(B,G,R) for any set of said three signals (B,G,R);
the coefficients K.sub.01, K.sub.02, K.sub.03 and k.sub.1 are positive real
numbers specified in accordance with said three signals B, G and R; and
C.sub.1 and C.sub.2 are constants specified by one of the color
transforming system and the image to be subjected to color transformation.
3. The color transforming method according to claim 1, wherein, when all of
said values of said three signals coincide and are expressed by a signal
value N, the signal value N is one of:
a linear function of a logarithm of a luminance L of the corresponding
gray, and expressed by N=C.sub.1 logL+c.sub.2 ; and
a linear function of a power of said luminance L of said corresponding
gray, and expressed by N=c.sub.1 L.gamma.+c.sub.2 ;
where the exponent .gamma. is a real number satisfying 0<.gamma.<1, and
c.sub.1 and c.sub.2 are constant.
4. The color transforming method according to claim 3, wherein:
said three signals represent any one of; equivalent neutral density,
integral equivalent neutral density, exposure density, logarithmic
exposure, colorimetric density, TV monitor signals, and signals by the
following set of equations:
N.sub.x =(X/X.sub.0).sup.1/3 =(L*+16)/116+a*/500
N.sub.y =(Y/Y.sub.0).sup.1/3 =(L*+16)/116
N.sub.z =(Z/Z.sub.0).sup.1/3 =(L*+16)/116-b*/200
where:
X, Y and Z are tristimulus values;
X.sub.0, Y.sub.0 and Z.sub.0 are the tristimulus values of a reference
white;
L* is a psychometric lightness for the L*a*b* color space; and
a* and b* are perceived psychometric chromaticities.
5. The color transforming method according to claim 1, wherein said
lightness component is one of a maximum value, a minimum value and a
median value of said three signals.
6. The color transforming method according to claim 1, wherein said input
image data are of an original scene or a original hardcopy image, and said
output image data are used to produce hardcopy images.
7. The color transforming method according to claim 6, wherein, when said
three signals are designated by (B2,G2,R2) and said three color
transformed signals by (B3,G3,R3) for each pixel, the transformation from
said three signals to said three color transformed signals is executed
using by the following set of equations:
B3=k.sub.0 (B2-A)+k.sub.1 (A-min (xy)A)+BW
G3=k.sub.0 (G2-A)+k.sub.1 (A-min (xy)A)+GW
R3=k.sub.0 (R2-A)+k.sub.1 (A-min (xy)A)+RW
where:
A is a function representing said lightness component specified for said
three signals (B2,G2,R2) and satisfying min{B2,G2,R2}.ltoreq.A.ltoreq.max
{B2,G2,R2};
k.sub.0 and k.sub.1 are constants;
(BW,GW,RW) represents the base density of the reflection medium; and
min(xy)A represents a minimum value of A for all pixels in the entire image
forming area.
8. The color transforming method according to claim 7, wherein:
said lightness component A is represented by any one of the equations:
A=min{B2,G2,R2},
A=max{B2,G2,R2},
and
A=median{B2,G2,R2},
where "median" is a function representing the second largest value for a
given set of (B2,G2,R2).
9. The color transforming method according to claim 7, wherein:
said original hardcopy image is a color positive image formed on a
transparent medium comprising at least three colorants, and
said constants k.sub.0 and k.sub.1 satisfy 0.7<k.sub.1 <k.sub.0 .ltoreq.1.
10. The color transforming method according to claim 7, wherein said
minimum value min(xy)A equals a constant between 0.0 and 0.3.
11. The color transforming method according to claim 6, wherein:
said original hardcopy image is a color positive image formed on a
transparent medium comprising at least three colorants;
said three signals represent integral equivalent neutral densities of three
colors obtained by a process comprising the steps of:
recording said color positive image with a scanner having three linearly
independent spectral sensitivities to produce original image signals for
each pixel,
transforming them to produce integral densities as measured by said
scanner, and
transforming said integral densities; and
said three color transformed signals represent the color transformed
integral equivalent neutral densities of the three colors and are
transformed to at least three second color transformed signals for
replication on the reflection medium.
12. The color transforming method according to claim 11, wherein;
the three linearly independent spectral sensitivities of said scanner are
designated by B, G and R,
said integral densities are represented by densities (B1, G1, R1) per
pixel,
said integral equivalent neutral densities of three colors are represented
by densities (B2, G2, R2) per pixel,
said color transformed integral equivalent neutral densities of three
colors are represented by densities (B3, G3, R3) per pixel, and
said second color transformed signals of three colors by densities (B4, G4,
R4) per pixel,
said integral densities (B1, G1, R1) per pixel are transformed to said
densities (B2, G2, R2) in accordance with the following set of equations
with the intermediary of a preliminarily constructed first lookup table
LUT1:
B2=LUT1.sub.B (B1)
G2=LUT1.sub.G (G1)
R2=LUT1.sub.R (R1);
said densities (B3, G3, R3) are transformed to said densities (B4, G4, R4)
in accordance with the following set of equations with the intermediary of
a preliminarily constructed second lookup table LUT2 and both densities
are output to a printer:
B4=LUT2.sub.B (B3)
G4=LUT2.sub.G (G3)
R4=LUT2.sub.R (R3);
when the densities (B4, G4, R4) are greater than the maximum density of
said reflection medium, said densities (B4, G4, R4) are clipped to said
maximum density; and
when the densities (B4, G4, R4) are smaller than the minimum density of
said reflection medium, said densities (B4, G4, R4) are clipped to said
minimum value.
13. The color transforming method according to claim 12, wherein:
said first lookup table LUT1 is constructed by a process comprising the
steps of:
preliminarily forming a gray scale on the transparent medium,
measuring the transmission density at more than one point by means of said
scanner and a densitometer having a fourth spectral sensitivity, and
plotting for each of B, G and R the transmission density from said scanner
on the horizontal axis and the transmission density from said densitometer
on the vertical axis; and
said second lookup table LUT2 is constructed by a process comprising the
steps of:
preliminarily forming a gray scale on the reflection medium,
measuring the reflection density at more than one point by means of said
scanner and said densitometer, and
plotting the reflection density from said scanner on the vertical axis and
the refelection density from said densitometer on the horizontal axis.
14. The color transforming method according to claim 12, wherein:
said first second lookup tables LUT1 and LUT2 are constructed by a process
comprising the steps of:
preliminarily measuring the spectral absorption waveforms of said three
colorants in said transparent and reflection media,
generating for more than one lightness value a spectral absorption waveform
which produces a gray under a light source S(.lambda.),
integrating the generated gray spectral absorption waveforms f(.lambda.),
by a spectral luminous efficiency curve V(.lambda.) and the spectral
absorption waveforms of the filters in said scanner B(.lambda.),
G(.lambda.) and R(.lambda.),
constructing data on optical densities D.sub.V, D.sub.B, D.sub.G and
D.sub.R in accordance with the following set of equations:
##EQU36##
and plotting the optical density D.sub.V on the vertical axis and optical
densities D.sub.B, D.sub.G on D.sub.R on the horizontal axis for each of
said transparent and reflection media.
15. The color transforming method as set forth in claim 1, wherein said
image input device is one of a scanner, a digital camera, a video camera,
a monitor, and a video projector, and said image output device is one of a
printer, a monitor, and a video projector.
16. The color transforming method as set forth in claim 1, wherein said
image input device is one of a scanner and a digital camera, and said
image output device is one of a printer and a monitor.
17. The color transforming method as set forth in claim 1, wherein said
image input device is a scanner and said image output device is a printer.
Description
BACKGROUND OF THE INVENTION
This invention relates to a color transforming method which intends to
achieve visually faithful or preferred color reproduction of color images.
More particularly, the invention relates to a color transforming method by
which input digital image data are converted to the image signals required
for the original image in an input (color space) system to be reproduced
faithfully in an output (color reproduction) system having a different
color gamut (color space) such as a different dynamic density range than
in the input (color space) system, as well as a color transforming method
for achieving transformation to image signals that are required to ensure
that the important colors are reproduced preferably, that is, in a
visually preferred lightness level, whether the input color space is the
same as the output color space or not. More specifically, the invention
relates to a color transforming method by which image signals read with a
scanner or the like from transmission or reflection original hardcopy
images obtained by photographing a subject on reversal films or negative
films, or image signals obtained by photographing a subject directly with
a solid-state imaging device such as a CCD, or image signals of an image
displayed on a TV monitor are converted to the digital signals that are
required for creating reproduced reflection hardcopy images visually
faithful to the transmission original hardcopy images, the subject, the
monitor and the like, or reproduced reflection hardcopy images on which
the important colors are reproduced in a visually preferred lightness
level, or for displaying reproduced softcopy images on the monitor or the
like which are visually faithful to the transmission originals, reflection
original, the subject and the like, or reproduced softcopy images on the
monitor or the like in which the important colors are reproduced in a
visually preferred lightness level.
In recent years, there is an increasing use of an image processing system
which involves the reading of an exposed film with a scanner and
subsequent conversion to digital image signals (the system is hereunder
referred to as a "hybrid system") and a digital image processing system in
which a subject is photographed with a digital camera or the like to
obtain digital image signals directly. The digital and hybrid systems
provide more flexibility in image processing than the analog system but,
on the other hand, they suffer from increased costs. Therefore, the
success of the hybrid and digital systems depends on whether the
improvement in image quality justifies the increased cost.
The hybrid system uses the same input original as in the analog system, so
in order to achieve an improvement in image quality, the image processing
procedure has to be reviewed in terms of zero base. This is also true with
the digital system. The image processing procedure can generally be
classified into three stages of setup, range compression (extension) and
design. These three elements of the image processing system have their own
counterparts in the visual perception as follows: setup can be compared to
luminance adaptation and chromatic adaptation, range compression
(extension) is similarly named in the visual perception, and design
modifications in the image processing system can be compared to retrieving
colors from memory and rendering preferred colors.
Among the three elements of the image processing system, setup and design
have been studied extensively to provide several important findings. On
the other hand, only few findings have so far been attained in the study
of range compression (extension). If studied at all, the range compression
is in many cases discussed in terms of the relationship between the
original scene and a hard copy but if the input range is sufficiently
wider than the output range, the input need not be the original scene. In
addition, from a practical viewpoint, the original scene is generally
difficult to measure. For these reasons, in the following discussion of
the prior art of range compression and its problems, we assume that a
reversal film is the original which is range compressed to a photographic
paper (hereunder "paper"). In order to circumvent the problem with setup,
we also assume that the input original is limited to what has been exposed
appropriately and in order to get around the problem with design, it is
assumed that the paper should reproduce an image which, as perceived by
the eye, is faithful to the original on the reversal film.
Speaking of the dynamic range, the paper is less flexible than the reversal
film and the former has typically a density range of about 2.0 whereas the
latter has a density range of about 3.0. Therefore, if the reversal film
is simply output, the highlights and shadows become "flat" (lose contrast)
to impair the image quality considerably. To deal with this problem, range
compression is required. However, if range compression merely involves
rendering the input original "less contrasty", the output picture is quite
poor in aesthetic appeal on account of the deteriorated contrast and
chroma. Thus, the reproduction of highlights and shadows and that of
contrast and chroma are tradeoffs.
To deal with this situation, two techniques are currently employed in
photography, printings and other areas of producing hardcopy images; one
technique involves rendering the input image less contrasty and restoring
the chroma by the "interlayer effect" or color correction, and the second
technique commonly called "dodging" involves printing with the shadows in
the exposed area being covered with a mask. However, these techniques have
their own limitations. In the former technique, the hue fidelity
deteriorates as the chroma improves and the skin color acquires a red
tinge. In other words, the reproduction of chroma and that of hue are
tradeoffs. Dodging which essentially involves a two-dimensional arithmetic
operation is low in operating efficiency and is not cost-effective.
Automatic dodging machines have recently been commercialized but the
problem of high calculation loads is still incumbent.
In color science, range compression (extension) is a subject which is
actively studied as part of gamut mapping on CIELab. Most of the studies
so far made depend on the combined use of compression and clipping but the
problem is that the timing of determining which method to use depends on
the graphics pattern.
Fidelity as perceived by the eye is also required by TV monitors, video
projectors and other machines that produce softcopy images; when subjects
photographed with digital cameras, video cameras, etc. or images on
transmission and reflection original hardcopy images as read with
scanners, etc. are to be displayed as reproduced softcopy images on TV
monitors, video projectors, etc. or when original softcopy image displayed
on TV monitors, video projectors, etc. are to be replicated on reflection
reproduced hardcopy images, it is required to reproduce output
softcopy/hardcopy images that are faithful to the input hardcopy/softcopy
as perceived with the eye. However, color gamut such as the dynamic
density range do not necessarily coincide between the input and output
spaces and the various problems described in the preceding paragraphs
exist.
In both the hybrid and digital systems, the color transformation process
for preparing reflection prints consists of gamma increasing and color
correction steps. In the gamma increasing step, the density contrast of a
reflection print is generally recommended to be higher than that of the
subject by a factor of 1.8 (if the reflection print is to be prepared from
the density data of a color negative film, the value should be increased
to 2.5 (.congruent.1.8/0.7) in consideration of the fact that the
characteristic curve of the color negative film has a gamma (.gamma.) of
0.7). The color correction step is often performed by the matrix operation
using for example a 3.times.3 or 3.times.9 color correcting matrix.
The color transforming process is commonly adapted to be performed in the
order of gamma increasing and color correction (see FIG. 9a) but the order
may be reversed such that color correction is performed first (FIG. 9b).
The process designs shown in FIGS. 9a and 9b generally yield different
results; however, if the gamma increasing is a linear process while the
color correction is expressed by a 3.times.3 matrix, the two operations
yield the same result as the following equation shows:
##EQU1##
In the color reproducing process, the colors of skin (face), green (grass)
and sky (blue) are called "important colors" and often require selective
processes for their reproduction. As for the reproduction of lightness, it
is generally recommended that the skin color be finished "light" (faint)
whereas the blue sky color "dark" (deep).
When an image formed on a copy or a first image forming medium is to be
replaced on a second image forming medium, complex color reproducing
processes have to be performed in order to ensure the preferred color
reproduction that appropriate color reproduction is compatible with the
selective reproduction of the important colors, in particular the skin and
sky colors, in a visually preferred lightness level. To this end, persons
having ordinary skill have carried out gradation modification in the field
of plate making and dodging or other processing in the field of
photography. Both the cases required highly skilled practice. Thus, there
has been a strong need for a method by which colors (important colors) can
be simply and selectively reproduced in a visually preferred lightness
level, while being properly reproduced in the replication of the image.
SUMMARY OF THE INVENTION
The present invention has been accomplished under these circumstances and
has as its first object providing a color transforming method by which an
output image faithful to an input image can be reproduced realtime and
very easily in an output color reproduction system different from an input
color space system.
A second object of the invention is to provide a color transforming method
that is capable of producing reproduced reflection hardcopy images or
reproduced softcopy images having an extremely high fidelity to
transmission original hardcopy images, subjects or original softcopy
images and which permits the required image processing to be executed
realtime and easily using a very simple processing system.
A third object of the invention is to provide a color transforming method
which, in addition to attaining the two stated objects, enables reproduced
reflection hardcopy images or reproduced softcopy images of good color and
density balances to be prepared realtime and easily by means of a very
simple processing system even if the input is transmission original
hardcopy images which are upset in color or density balance or original
image signals which are not appropriate in terms of exposure or display
conditions.
A fourth object of the invention is to satisfy the above-mentioned need of
the prior art by providing a color transforming method capable of
achieving the preferred color reproduction, by which the important colors,
in particular the skin and sky colors are elicited from the hue
information in an input color space system and the lightness of these
colors is controlled in a selective and very simple manner and finished to
a visually preferred lightness level while, at the same time, the colors
of an input image can be properly reproduced on the output image, in an
output color reproducing system of which the color gamut is the same as or
different from that of the input color space system.
In other words, the preferred color reproduction to be achieved is based on
the faithful color reproduction of the input image, but intentionally
deviated from the faithful color reproduction as to the important colors,
which are to be reproduced in a visually preferred manner.
A fifth object of the invention is to provide a color transforming method
which is capable of outputting a reproduced reflection hardcopy image or a
reproduced softcopy image on which the colors of a transmission original
hardcopy image, subject or original softcopy image are properly
reproduced, with the important colors being selectively finished to a
visually preferred lightness level and which is capable of executing the
necessary image processing procedures by a simple processing system in a
realtime and convenient manner.
According to a first embodiment of the invention, the stated objects can be
attained by a color transformation method in which input image data
represented by three signals that mutually independent and provide a color
of gray when values of three signals are subjected to color transformation
to produce output image data represented by three color transformed
signals, which method comprises the steps of determining for each pixel a
lightness component specified between a maximum and a minimum value for
said three signals and chromaticity components obtained by excluding said
lightness component from said three signals, amplifying or attenuating the
thus obtained chromaticity components in accordance with said three
signals and adding them to said lightness component amplified or
attenuated in accordance with said three signals.
When said three signals are designated by (B,G,R) and said three color
transformed signals by (B',G',R') for each pixel, the color transformation
from said three signals to said three color transformed signals is
preferably represented by the following set of equations (1):
B'=K.sub.01 {B-f(B,G,R)}+k.sub.1 {f(B,G,R)-C.sub.1 ]+C.sub.2
G'=K.sub.02 {G-f(B,G,R)}+k.sub.1 {f(B,G,R)-C.sub.1 ]+C.sub.2
R'=K.sub.03 {R-f(B,G,R)}+k.sub.1 {f(B,G,R)-C.sub.1 ]+C.sub.2(1)
where f(B,G,R) is a function that satisfies
min(B,G,R).ltoreq.f(B,G,R).ltoreq.max(B,G,R) for any set of said three
signals (B,G,R); the coefficients K.sub.01, K.sub.02, K.sub.03 and k.sub.1
are positive real numbers specified in accordance with said three signals
B, G and R; and C.sub.1 and C.sub.2 are constants specified by the color
transforming system or the image to be subjected to color transformation.
Preferably, all of the coefficients K.sub.01, K.sub.02 and K.sub.03 take
the same value k.sub.0 (k.sub.0 >0).
When all of the numerical values of the respective three signals coincide
and are expressed by a signal value N, the signal value N is preferably a
linear function of a logarithm or a power of a luminance L of the
corresponding gray, and expressed by the following equation (2) or (3),
respectively:
N=c.sub.1 logL+c.sub.2 (2)
N=c.sub.1 L.sup..gamma. c.sub.2 (3)
where the exponent .gamma. is a real number satisfying 0<.gamma.<1, and
c.sub.1 and c.sub.2 are constant.
Preferably, the three signals represent any one of equivalent neutral
density, integral equivalent neutral density, exposure density,
logarithmic exposure, calorimetric density, TV monitor signals or those
represented by the following set of equations (4):
N.sub.X =(X/X.sub.0).sup.1/3 =(L*+16)/116+a*/500
N.sub.Y =(Y/Y.sub.0).sup.1/3 =(L*+16)/116
N.sub.Z =(Z/Z.sub.0).sup.1/3 =(L*+16)/116-b*/200 (4)
where X, Y and Z are tristimulus values and X.sub.0, Y.sub.0 and Z.sub.0
are the tristimulus values of a reference white; and L* is a psychometric
lightness for the L*a*b* color space; and a* and b* are perceived
psychometric chromaticities.
Preferably, said lightness component is a maximum value, a minimum value or
a median value of said three signals.
Preferably, the image data are setup image data obtained by adjustment of
brightness and/or white balance.
Preferably, in a second embodiment of the invention, said input image data
are captured or scanned data of original scene or original hardcopy image,
and said output image data are image data to produce hardcopy images.
Or, according to a second embodiment of the invention, the stated objects
can be attained by a color transforming method in which a subject or an
original image formed on a transparent medium comprising at least three
colorants is replicated on a reflection medium comprising at least three
colorants, which method comprises the steps of:
transforming said subject or said original image to signals the three
values of which coincide for a plurality of colors visually perceived as
gray for each pixel and which are on a logarithmic scale with respect to
the intensity of light;
using the obtained three signals for each pixel to determine a single
lightness component specified between their maximum and minimum values and
a chromaticity component obtained by excluding said lightness component
from each of said three signals;
amplifying or attenuating the thus obtained three chromaticity components
in accordance with said three signals and also amplifying or attenuating
said lightness component in accordance with said three signals and
thereafter adding the thus amplified or attenuated lightness component to
each of said amplified or attenuated three chromaticity components so as
to transform them to three (first) color transformed signals; and
thereafter
transforming said three (first) color transformed signals to at least three
second color transformed signals for replication on said reflection
medium.
When said three signals are designated by (B2,G2,R2) and said three (first)
color transformed signals by (B3,G3,R3) for each pixel, the transformation
from said three signals to said three (first) color transformed signals is
preferably executed by the following set of equations (5):
B3=k.sub.0 (B2-A)+k.sub.1 (A-min.sub.(xy) A)+BW
G3=k.sub.0 (G2-A)+k.sub.1 (A-min.sub.(xy) A)+GW
R3=k.sub.0 (R2-A)+k.sub.1 (A-min.sub.(xy) A)+RW (5)
where A is a function that represents said lightness component specified
for said three signals (B2,G2,R2) and which satisfies
min{B2,G2,R2}.ltoreq.A .ltoreq.max{B2,G2,R2}; k.sub.0 and k.sub.1 are
constants; (BW,GW,RW) represents the base density of the reflection
medium; and min.sub.(xy) A represents a minimum value of A for all pixels
in the entire image forming area.
Preferably, said lightness component A is represented by any one of the
equations: A=min{B2,G2,R2}, A=max{B2,G2,R2} and A=median {B2,G2,R2}, where
"median" is a function representing the second largest value for a given
set of (B2,G2,R2).
Preferably, said hardcopy original image is a color positive image formed
on a transparent medium comprising at least three colorants and said
constants k.sub.0 and k.sub.1 satisfy 0.7<k.sub.1 <k.sub.0 .ltoreq.1.
If said minimum value min.sub.(xy) A is to be replaced by a constant, it is
preferably a constant between 0.0 and 0.3, more preferably between 0.1 and
0.2.
In another preferred case, said original hardcopy image is a color positive
image formed on a transparent medium comprising at least three colorants,
said three signals represent equivalent neutral densities of three colors
obtained by a process comprising recording said color positive image with
a scanner having three linearly independent spectral sensitivities to
produce original image signals for each pixel, transforming them to
produce analytical densities as measured by said scanner and transforming
said analytical densities, and said three (first) color transformed
signals represent the color transformed equivalent neutral densities of
the three colors and are transformed to at least three second color
transformed signals for replication on the reflection medium.
In yet another preferred case, said hardcopy original image is a color
positive image formed on a transparent medium comprising at least three
colorants, said three signals represent integral equivalent neutral
densities of three colors obtained by a process comprising recording said
color positive image with a scanner having three linearly independent
spectral sensitivities to produce original image signals for each pixel,
transforming them to produce integral densities as measured by said
scanner and transforming said integral densities, and said three (first)
color transformed signals represent the color transformed integral
equivalent neutral densities of the three colors and are transformed to at
least three second color transformed signals for replication on the
reflection medium.
In a still preferred case, said three signals represent integral equivalent
neutral densities of three colors obtained by a process comprising
directly recording said subject with a solid-state imaging device having
three linearly independent spectral sensitivities to produce original
image signals for each pixel, transforming them to produce exposure
densities dependent on said solid-state imaging device and transforming
said exposure densities, and said three (first) color transformed signals
represent the color transformed integral equivalent neutral densities of
the three colors and are transformed to at least three second color
transformed signals for replication on the reflection medium.
In another preferred case, said three signals represent integral equivalent
neutral densities of three colors obtained by a process comprising
photographing said subject on a color negative film having three linearly
independent spectral sensitivities, transforming said photographed subject
to exposure densities per pixel dependent on said color negative film by
means of an auxiliary scanner or solid-state imaging device, and
transforming said exposure densities, and said three (first) color
transformed signals represent the color transformed integral equivalent
neutral densities of the three colors and are transformed to at least
three second color transformed signals for replication on the reflection
medium.
If the three linearly independent spectral sensitivities of said scanner
(solid-state imaging device or color negative film) are designated by B, G
and R, said (analytical) integral (or exposure) densities by densities
(B1,G1,R1) per pixel, (said equivalent neutral densities of three colors
or) said integral equivalent neutral densities of three colors by
densities (B2,G2,R2) per pixel, (said first color transformed equivalent
neutral densities of three colors or) said (first) color transformed
integral equivalent neutral densities of three colors by densities
(B3,G3,R3) per pixel, and said second color transformed signals of three
colors by densities (B4,G4,R4) per pixel, it is preferred that said
integral densities (B1,G1,R1) per pixel are transformed to said densities
(B2,G2,R2) in accordance with the following set of equations (6) with the
intermediary of a preliminarily constructed first lookup table LUT1:
B2=LUT1.sub.B (B1)
G2=LUT1.sub.G (G1)
R2=LUT1.sub.R (R1) (6)
whereas said densities (B3,G3,R3) are transformed to said densities
(B4,G4,R4) in accordance with the following set of equations (7) with the
intermediary of a preliminarily constructed second lookup table LUT2 and
both densities are output to a printer:
B4=LUT2.sub.B (B3)
G4=LUT2.sub.G (G3)
R4=LUT2.sub.R (R3) (7)
provided that if the densities B4, G4 and R4 are greater than the maximum
density of said reflection medium or smaller than its minimum density, the
densities are clipped to said maximum or minimum value respectively.
Alternatively, instead of determining said densities (B2,G2,B2) by direct
conversion from said densities (B1,G1,R1) with the intermediary of said
first lookup table LUT1 said densities (B2,G2,R2) are preferably
determined by first transforming said densities (B1,G1,R1) per pixel to
integral equivalent neutral densities of three colors
(B2.sub.01,G2.sub.0,R2.sub.0) in accordance with the following set of
equations (8) with the aid of said first lookup table LUT1:
B2.sub.0 =LUT1.sub.B (B1)
G2.sub.0 =LUT1.sub.G (G1)
R2.sub.0 =LUT1.sub.R (R1) (8)
and then performing setup in accordance with the following set of equations
(9):
B2=B2.sub.0 -BS+AS
G2=G2.sub.0 -GS+AS
R2=R2.sub.0 -RS+AS (9)
where BS, GS and RS are values satisfying the following relations:
min.sub.(xy) B2.sub.0 .ltoreq.BS.ltoreq.max.sub.(xy) B2.sub.0
min.sub.(xy) G2.sub.0 .ltoreq.GS.ltoreq.max.sub.(xy) G2.sub.0
min.sub.(xy) R2.sub.0 .ltoreq.RS.ltoreq.max.sub.(xy) R2.sub.0
where min.sub.(xy) B2.sub.0, min.sub.(xy) G2.sub.0 and min.sub.(xy)
R2.sub.0 represent the minimal values of B2.sub.0, G2.sub.0 and R2.sub.0
for all the pixels in the entire image forming area; max.sub.(xy)
B2.sub.0, max.sub.(xy) G2.sub.0 and max.sub.(xy) R2.sub.0 represent the
maximal values of B2.sub.0, G2.sub.0 and R2.sub.0 for all the pixels in
the entire image forming area; and AS is a real number specified in
accordance with BS, GS and RS.
In another preferred case, said first lookup table LUT1 is constructed by a
process comprising preliminarily forming a a gray scale on the transparent
medium, measuring the transmission density at more than one point by means
of both said scanner and a densitometer having a fourth spectral
sensitivity and plotting for each of B, G and R the transmission density
from said scanner on the horizontal axis and the transmission density from
said densitometer on the vertical axis, and said second lookup table LUT2
is constructed by a process comprising preliminarily forming a gray scale
on the reflection medium, measuring the reflection density at more than
one point by means of both said scanner and said densitometer and plotting
the reflection density from said scanner on the vertical axis and the
reflection density from said densitometer on the horizontal axis.
Said densitometer is preferably a visual densitometer.
Alternatively, said densitometer may preferably be replaced by any one of
B, G and R in said scanner.
In yet another preferred case, said first and second lookup tables LUT1 and
LUT2 are constructed by a process comprising preliminarily measuring the
spectral absorption waveforms of said three colorants in said transparent
and reflection media, generating for more than one lightness value a
spectral absorption waveform which produces a gray under a light source
s(.lambda.), integrating the generated gray spectral absorption waveforms,
which may each be written as f(.lambda.), by a spectral luminous
efficiency curve V(.lambda.) and the spectral absorption waveforms of thee
filters in said scanner B(.lambda.), G(.lambda.) and R(.lambda.),
constructing data on optical densities D.sub.V, D.sub.B, D.sub.G and
D.sub.R in accordance with the following set of equations (10), and
plotting the optical density D.sub.V on the vertical axis and optical
densities D.sub.B, D.sub.G and D.sub.R on the horizontal axis for each of
said transparent and reflection media:
##EQU2##
Preferably, said first lookup table performs an identity transformation and
said second lookup table is constructed by plotting the integral and
visual densities on the horizontal and vertical axes, respectively, which
are dependent on the spectral sensitivities of said solid-state imaging
device or said color negative film in relation to the gray scale formed on
the reflection medium.
According to a third embodiment of the invention, the stated objects can be
attained by a color transforming method in which the color image formed on
a first medium is replicated on a second medium with said first and second
media being managed in terms of integral equivalent neutral densities
dependent on at least three independent spectral sensitivities and with
either color gamut transformation or color correction or both being
performed with the intermediary of said integral equivalent neutral
densities. Preferably, the integral equivalent neutral densities are such
that a signal value for the case where all numerical values for the
respective elements coincide is a linear function of the logarithm or
power number of a luminance corresponding to that signal value, provided
that the exponent .gamma. is a real number satisfying 0<.gamma.<1.
According to a fourth embodiment of the invention, the stated objects can
be attained by a color transforming method in which a subject is
replicated on a medium by transforming the subject to exposure densities
at three or more independent spectral sensitivities, managing the medium
in terms of an integral equivalent neutral densities dependent on said
spectral sensitivities and performing either color gamut transformation or
color correction or both on said exposure densities with the intermediary
of said integral equivalent neutral densities. Preferably, the exposure
densities and the integral equivalent neutral densities are such that a
signal value for the case where all numerical values for the respective
elements coincide is a linear function of the logarithm or power number of
a luminance corresponding to that signal value, provided that the exponent
.gamma. is a real number satisfying 0<.gamma.<1.
The gray scale or gray which are used in constructing the first lookup
table LUT1 and the second lookup table LUT2 is either one of the visually
most preferred grays which are a little shifted from calorimetric gray to
the negative side of the b* axis in the L*a *b* space or the colorimetric
gray.
It is also preferred that the densities VW on a densitometer in relation to
the base of said reflection medium rather than the base density values
(BW, GW, RW) of the reflection medium is measured and the densities
(VW,VW,VW) are substituted.
According to a first case of a fifth embodiment of the invention, the
stated objects can be attained by a color transforming method in which in
the color transformation of a color image represented by color signals
consisting of components corresponding to blue (B), green (G) and red (R),
the color signals for each pixel are transformed using a coefficient that
takes a relatively small value when the hue corresponding to said color
signals for each pixel is yellow red, and a relatively large value when
the hue is cyan blue. Said coefficient is a function of said color signals
(B,G,R) for each pixel.
Said color signals for each pixel take preferably values satisfying B>G>R
when the hue corresponding thereto is yellow red, and values satisfying
B<G<R when the hue is cyan blue.
Said transforming coefficient is preferably a function which includes at
least one of (R-A), (A-B), (R-G), (R-B) and (G-B) where the symbol A is a
function of said color signals (B,G,R) for each signal which satisfies the
following equation (11):
min (B,G,R).ltoreq.A.ltoreq.max (B,G,R) (11)
Said function is preferably a linear function.
The symbol A satisfies preferably the following equation (12):
min (B,R)<A<max (B,R) (12)
The symbol A is preferably a median value of said color signals (B,G,R) for
each pixel.
Said transforming coefficient is preferably a coefficient k of gamma
increasing which is expressed by the following equation (13), provided
that said color signals are written as (B,G,R) and the processed color
signals as (B',G',R'):
##EQU3##
where C.sub.1 and C.sub.2 are constants specified by the color
transforming system or the image to be subjected to color transformation.
Said transforming coefficient is preferably a coefficient k.sub.1 of gamma
increasing which is expressed by the following equation (14), provided
that said color signals are written as (B,G,R) and the processed color
signals as (B',G',R'):
B'=k.sub.01 (B-A)+k.sub.1 (A-C.sub.1)+C.sub.2
G'=k.sub.02 (G-A)+k.sub.1 (A-C.sub.1)+C.sub.2
R'=k.sub.03 (R-A)+k.sub.1 (A-C.sub.1)+C.sub.2 (14)
where the coefficients k.sub.01, k.sub.02 and k.sub.03 are positive real
numbers specified in accordance with the color signals; C.sub.1 and
C.sub.2 are constants specified by the color transforming system or the
image to be subjected to color transformation; and A is a function of the
color signals (B,G,R) for each signal which satisfies the following
equation (11):
min (B,G,R).ltoreq.A.ltoreq.max (B,G,R) (11)
When all of the numerical values of the respective elements (B,G,R) of said
color signals coincide and are expressed by a signal value N, the signal
value N is preferably a linear function of the logarithm of L, or the
luminance of the corresponding gray, and expressed by the following
equation (2):
N=c.sub.1 logL+c.sub.2 (2)
where c.sub.1 and c.sub.2 are constants.
Preferably, said color signals represent any one of equivalent neutral
density, integral equivalent neutral density, exposure density,
logarithmic exposure and calorimetric density.
When all of the numerical values of the respective elements (B,G,R) of said
color signals coincide and are expressed by a signal value N, the signal
value N is preferably a linear function of the power number of L, or the
luminance of the corresponding gray, and represented by the following
equation (3):
N=c.sub.1 L.sup..gamma. +c.sub.2 (3)
where the exponent .gamma. is a real number satisfying 0<.gamma.<1 and
c.sub.1 and c.sub.2 are constants.
Said color signals are preferably TV monitor signals.
Preferably, said color signals are setup color signals obtained by
adjustment of brightness and/or white balance.
According to a second case of the fifth embodiment of the invention, the
stated objects can be attained by a color transforming method in which in
the color transformation of a color image represented by color signals
consisting of components corresponding to blue (B), green (G) and red (R),
the color signals for each pixel are transformed using a coefficient that
takes a relatively small value when said color signals for each pixel take
values satisfying B>G>R, and a relatively large value when B<G<R is
satisfied. Said coefficient is a function of said color signals (B,G,R)
for each pixel.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a flowchart illustrating a color transforming method according to
an embodiment of the invention;
FIG. 2 is a flowchart illustrating a color transforming method according to
another embodiment of the invention;
FIG. 3 is a flowchart illustrating a color transforming method according to
yet another embodiment of the invention;
FIG. 4 is a graph exemplifying grays preferred for use in constructing the
lookup tables to be used in the color transforming method of the
invention; and
FIG. 5 is a flowchart illustrating a color transforming method according to
still another embodiment of the invention;
FIG. 6 is a flowchart illustrating a color transforming method according to
another embodiment of the invention;
FIG. 7 is a flowchart illustrating yet another embodiment of the invention;
FIGS. 8a and 8b illustrate two exemplary systems for implementing the color
transforming method of the invention.
FIGS. 9a and 9b illustrate two conventional schemes for performing color
transformation.
DETAILED DESCRIPTION OF THE INVENTION
The color transforming method of the invention will now be described in
detail with reference to the preferred embodiments shown in the
accompanying drawings.
To begin with, the color transforming method according to the second
embodiment of the invention is described. FIG. 1 is a flowchart
illustrating the color transforming method according to the second
embodiment of the invention. As shown, the color transforming method
according to the second embodiment of the invention comprises
photoelectric scanner reading of an image on a transmission original such
as a color positive image exposed on a reversal film, recording the image
as original image signals per pixel, and transforming them to signals the
three values of which coincide for a plurality of colors visually
perceived as gray for each pixel and which are on a logarithmic scale with
respect to the intensity of light, as exemplified by equivalent neutral
density (hereunder sometimes abbreviated as END) or an integral density
extended from this equivalent neutral density which is an analytical
density (said extended density is hereunder referred to as an integral
equivalent neutral density or integral END).
In the following description of the second embodiment of the invention, the
input image on the hardcopy or softcopy is a color positive image on a
reversal film; however, the invention is in no way limited to this
particular hardcopy and any input will suffice if it can be transformed to
the above-defined signals such as END and integral END (hereunder
sometimes abbreviated as IND). For example, the invention is also
applicable to a system in which a subject is directly imaged with a
solid-state imaging device such as CCD, more specifically a digital camera
or a video camera, to record it as digital image signals, which are then
output on a reflective print, as well as to a system in which a subject is
photographed on a color negative film and the resulting color negative
image is read with a scanner or CCD to record it as digital image signals,
which are then output on a reflective print. In the following description,
IND is taken as a representative example of signals the three values of
which coincide for a plurality of colors visually perceived as gray for
each pixel and which are on a logarithmic scale with respect to the
intensity of light. In the following description, the three primaries,
blue (B), green (G) and red (R), are also taken as a typical example of
three linearly independent colors so that IND is designated by D.sub.B,
D.sub.G and D.sub.R. It should, however, be noted that this is not the
sole case of the invention and the combinations of cyan (C), magenta (M)
and yellow (Y) or any other three linearly independent colors may of
course be substituted.
The next step is a characterizing portion of the invention method and a
lightness component and chromaticity components of the respective colors
are computed from IND, or D.sub.B, D.sub.G and D.sub.R.
As already mentioned in connection with the prior art, it is desirable for
range compression to be performed in such a way as to satisfy four
requirements, i.e., description of highlights and shadows and the
preservation of contrast, chroma and hue. In spite of these four
requirements to be satisfied, the degrees of freedom that are allowed are
three B, G and R. In other words, if the four requirements are independent
of one another, they cannot be satisfied simultaneously. In range
compression, it is critical to determine which are possible and which are
not. In the present invention, fidelity to originals (hardcopy or softcopy
images), especially color transparency hardcopy images, is of prime
importance, so the preservation of hues and the description of highlights
and shadows are performed. For the sake of simplicity, the following
description assumes the use of a system of block dyes which have
rectangular absorption waveforms and which produce a gray when the
densities of B, G and R coincide.
According to color science, hues are given by an antilogarithmic number
ratio B:G:R, so in order to preserve hues in terms of density (on a
logarithmic scale), one may preserve the density difference between B and
G or between G and R. Hence, two degrees of freedom are lost at the cost
of hue preservation. Further, the visual perception has such attributes
that most of the colors in highlights and shadows are achromatic or
near-achromatic. Therefore, if it is possible to extract only the
achromatic component of a given color and compress it (render it less
contrasty), one may well expect that the description of highlights and
shadows can be realized.
Thus, if any given color is separated into a chromaticity component and a
lightness component and the former is preserved while the latter is
compressed, one can accomplish both the preservation of the hue and the
description of the highlights and shadows. Based on this understanding, we
write the BGR densities of a given color as (D.sub.B, D.sub.G, D.sub.R)
and its lightness as D.sub.A and decompose the (D.sub.B, D.sub.G, D.sub.R)
into the following equation (15):
##EQU4##
where the first term of the right side may be interpreted as representing
the chromaticity components whereas the second term as the lightness
component.
In this way, the BGR densities of a given color (D.sub.B, D.sub.G, D.sub.R)
are decomposed into the chromaticity components in the first term and the
lightness component in the second term. Then, the above-described image
processing for compressing the lightness component D.sub.A is expressed by
the following equation (16) and one can compute the BGR densities
subjected to first color transformation (color space compression), namely,
the integral END (D.sub.rB, D.sub.rG, D.sub.rR) subjected to first color
transformation (hereunder referred to simply as "color correction"):
##EQU5##
where k is a compression coefficient satisfying 0<k<1.
If the setup condition which requires the brightest point in the reversal
original (hardcopy) image to coincide with the white background D.sub.rW
of the paper which is a reflection medium is taken into account, the
following equation (17) holds:
##EQU6##
where min.sub.(xy) D.sub.A represents the minimal value of D.sub.A for all
the pixels in the entire image forming area. For the sake of simplicity,
the equation (17) is hereunder rewritten in the following simplified form:
D.sub.ri =D.sub.i -D.sub.A +k(D.sub.A -min.sub.(xy) D.sub.A)+D.sub.rW,
or
D.sub.ri (x,y)=D.sub.i (x,y)-D.sub.A (x,y)+k{D.sub.A (x,y)-min.sub.(xy)
D.sub.A (x,y)}+D.sub.rW
where the subscript i represents B, G or R.
This equation actually satisfies the above-described requirements as will
be apparent from the following equation (18) which holds for any value of
i.noteq.j:
D.sub.ri -D.sub.rj =(D.sub.i -D.sub.A +kD.sub.A -kmin.sub.(xy) D.sub.A
+D.sub.rW)-(D.sub.j -D.sub.A +kD.sub.A -kmin.sub.(xy) D.sub.A
+D.sub.rW)=D.sub.i -D.sub.j (18)
Obviously, the difference in density is preserved independently of the
definition of lightness. Further, the lightness component has been
compressed since D.sub.rA =kD.sub.A <D.sub.A or D.sub.rA =k(D.sub.A
-min.sub.(xy) D.sub.A)<D.sub.A. Therefore, if the lightness D.sub.A is
defined in some way, the algorithm for the color transforming method of
the invention can be established. The definition of lightness will be
described more specifically below.
When the color corrected integral END densities (D.sub.rB, Dr.sub.G,
D.sub.rR) have been thusly computed as signals in which only the lightness
component (D.sub.A -min.sub.(xy) D.sub.A) is compressed, the density
signals (D.sub.rB, D.sub.rG, Dr.sub.rR) are converted to output image
signals (device dependent data) which are dependent on the printer (i.e.,
the reflection medium used with the printer) and on the at least three
colorants formed on the reflection medium, and the printer then yields a
reproduced reflection image as a replication of the image from the
transmission original hardcopy image onto the reflection medium. The
reproduced image thus replicated on the reflection medium features
faithful reproduction of the image from the transmission original hardcopy
image, in which the hues are preserved adequately, the highlights and
shadows are fully described and only the lightness component has been
compressed.
We now describe the method of setting the lightness component D.sub.A. In
the present invention, given a set of densities (D.sub.B, D.sub.G,
D.sub.R) the lightness component D.sub.A is preferably expressed in terms
of the maximum, minimum or median value of each of the densities D.sub.B,
D.sub.G and D.sub.R. If the maximum value is used, D.sub.A is expressed as
max(D.sub.B, D.sub.G, D.sub.R); in the case of the minimum value, D.sub.A
is expressed as min(D.sub.B, D.sub.G, D.sub.R); for the median value,
D.sub.A is expressed as median(D.sub.B, D.sub.G, D.sub.R). The "median"
designates a function for representing the second largest (or smallest)
value for the given set of densities (D.sub.B, D.sub.G, D.sub.R).
In accordance with common knowledge in color science, the lightness D.sub.A
should be defined as:
D.sub.A =-log{0.1.multidot.T.sub.B +0.6.multidot.T.sub.G
+0.3.multidot.T.sub.R }
=-log{0.1.multidot.10.sup.-DB +0.6.multidot.10.sup.-DG
+0.3.multidot.10.sup.-DR }
However, this definition is not universal enough to explain all visual
phenomena. For example, the Helmholtz-Kohlrausch effect, the Hunt effect
and the Bezold-Brucke effect cannot be explained by this definition. Many
various models on lightness have so far been reviewed but as of today no
single model has been found that can explain all visual phenomena.
Therefore, in the present invention, lightness is defined in terms of zero
base.
Returning to the lightness D.sub.A, it must at least satisfy the following
inequality:
min{D.sub.B, D.sub.G, D.sub.R }.ltoreq.D.sub.A .ltoreq.max{D.sub.B,
D.sub.G, D.sub.R }
First, in order to secure the maximum and minimum values, both min{D.sub.B,
D.sub.G, D.sub.R } and max{D.sub.B, D.sub.G, D.sub.R } maybe adopted as
definitions of lightness.
To those who are familiar with the CIE color system, this may be a rather
strange way to define lightness but from the stand-point of the Ostwald
system in which all colors are described in terms of the ratio between
white, black and pure colors, this is a quite natural way. Thus,
min{D.sub.B, D.sub.G, D.sub.R } corresponds to the black content and
max}D.sub.B, D.sub.G, D.sub.R } to the white content.
It should be noted here that the Ostwald system is dealt with as a base in
the German Industrial Standards (DIN) whereas min{D.sub.B, D.sub.G,
D.sub.R } is called "under color" in the printing industry and used to
create a black printer (for under color removal or UCR). In this sense,
both definitions are well established in the art.
Yet these definitions refer to the maximum and minimum values that can be
taken by lightness and there is no denying that lightness is either
overestimated or underestimated. To deal with this problem, we derive a
third definition of lightness a posteriori from the appearances of colors.
If lightness D.sub.A is specified, a chromaticity vector .DELTA.D.sub.i is
determined by the following equation (19):
##EQU7##
If .DELTA.D.sub.B, .DELTA.D.sub.G and .DELTA.D.sub.R are assumed to have
the following correlationships in interpretation with three primary colors
and gray:
.DELTA.D.sub.B >0Y (yellow), .DELTA.D.sub.G >0M (magenta),
.DELTA.D.sub.R >0C (cyan)
.DELTA.D.sub.B =0N (neutral), .DELTA.D.sub.G =0neutral,
.DELTA.D.sub.R =0neutral
.DELTA.D.sub.B <0B (blue), .DELTA.D.sub.G <0G (green),
.DELTA.D.sub.R <0R (red)
any chromaticity vector can be correlated to color interpretation. In the
above correlationships, the designation P.fwdarw.Q refers to the
proposition that "Q if P". The color interpretation system under
discussion is characterized by the following two features: no two
interpretations that are complementary to each other appear
simultaneously; and only two hues that are adjacent on a hue circle can
appear simultaneously. This is a model of interpretations that is
essentially equivalent to the model of opponent colors which Hering
postulated in connection with the color appearance.
If lightness is specified according to this interpretation system, the
interpretation of a given color, or its appearance, is determined. For
example, if lightness D.sub.A is defined as min{D.sub.B, D.sub.G, D.sub.R
}, the skin color is interpreted as follows. Noting D.sub.B >D.sub.G
>D.sub.R, we obtain
##EQU8##
Hence, the skin color is interpreted as yellow magenta on the assumption
of D.sub.A =min.sub.(xy) D.sub.i. Thus, the interpretation of chromaticity
is specified if lightness is specified; conversely, if the interpretation
of chromaticity is specified, the definition of lightness is derived.
In terms of color perception, the skin color is apparently perceived as
yellow red; hence, the following relationship must be satisfied:
##EQU9##
Speaking of yellow green, it is literally perceived as yellow green; hence:
##EQU10##
The color of blue sky is perceived as cyan blue; hence:
##EQU11##
In other words, lightness compatible with color appearance can be defined
by adopting the definition of lightness which satisfies the following
relationships:
skin color.fwdarw.D.sub.B >D.sub.G >D.sub.R .fwdarw.D.sub.A =D.sub.G
yellow green.fwdarw.D.sub.B >D.sub.R >D.sub.G .fwdarw.D.sub.A =D.sub.R
blue sky color.fwdarw.D.sub.R >D.sub.G >D.sub.B .fwdarw.D.sub.A =D.sub.G
It is therefore necessary to give the thus defined lightness as a
calculable function and the lightness D.sub.A which provides the
above-described interpretation is none other the median value of {D.sub.B,
D.sub.G, D.sub.R }. Therefore, the median value of {D.sub.B, D.sub.G,
D.sub.R } can be set as lightness D.sub.A for the purposes of the
invention. In the field of numerical analysis, arithmetic operations to
give the median value are called "median" operations and in compliance
with this convention, the following notation is adopted in the present
invention:
D.sub.A =median{D.sub.B, D.sub.G, D.sub.R }
For the sake of simplicity, color compression will be named differently in
the following description, depending upon the definition of lightness
D.sub.A. If D.sub.A =max{D.sub.B, D.sub.G, D.sub.R }, the compression is
OCC (Over Color Compression); if D.sub.A =median{D.sub.B, D.sub.G, D.sub.R
}, MCC (Median Color Compression) is used; if D.sub.A =min{D.sub.B,
D.sub.G, D.sub.R }, the name to be used is UCC (Under Color Compression).
Thus, the lightness component D.sub.A can be set. The foregoing description
is simplified in that densities D.sub.B, D.sub.G and D.sub.R, as well as
lightness D.sub.A in the system of block dyes are used to define END and
integral END for the same system. It should, however, be noted that the
above description is also valid for actual colorants which are not block
dyes and it is with such actual colorants, not the block dyes, that the
END and integral END used in the present invention should work
effectively.
In the foregoing example, the densities (D.sub.B, D.sub.G, D.sub.R) given
as the lightness component are illustrated by max(D.sub.B, D.sub.G,
D.sub.R) or min(D.sub.B, D.sub.G, D.sub.R) or median(D.sub.B, D.sub.G,
D.sub.R); however, these are not the sole examples of the invention and
any function will suffice as long as it satisfies min(D.sub.B, D.sub.G,
D.sub.R).ltoreq.D.sub.A .ltoreq.max(D.sub.B, D.sub.G, D.sub.R). For
example, D.sub.A may be expressed by the average of densities D.sub.B,
D.sub.G and D.sub.R, namely, 1/3(D.sub.B +D.sub.G +D.sub.R).
In the invention, the preservation of hues and the description of
highlights and shadows are performed positively; on the other hand, the
chroma is not preserved correctly but tends to become somewhat higher than
what it should be. Since the slight increase in chroma is generally
preferred from the viewpoint of visual perception, the equation (17)
should suffice for performing the transformation which is the most
characterizing aspect of the invention. However, if there is the need for
chroma adjustment, the equation (17) is preferably replaced by the
following equation (20) using parameters k.sub.0 and k.sub.1 which satisfy
0<k.sub.1 <k.sub.0 .ltoreq.1:
D.sub.ri =k.sub.0 (D.sub.i -D.sub.A)+k.sub.1 (D.sub.A -min.sub.(xy)
D.sub.A)+D.sub.rW
D.sub.ri (x,y)=k.sub.0 {D.sub.i (x,y)-D.sub.A (x,y)}+k.sub.1 {D.sub.A
(x,y)-min.sub.(xy) D.sub.A (x,y)}+D.sub.rW (20)
where parameter k.sub.1 is a compression coefficient which has the same
meaning as compression coefficient k in the equation (17).
Parameter k.sub.1 (or k) which is also referred to as a lightness
coefficient may be set at appropriate values that satisfy 0<k.sub.1
(k)<1.0 in accordance with the dynamic density range of the input image on
the hardcopy or softcopy (e.g. a color positive image on a reversal film)
or the subject, as well the dynamic range of the densities that can be
reproduced on the output reflection print. Considering the dynamic density
range ratio for the case where the image on a reversal film is output as a
reflection print, human vision and other factors, the parameter k.sub.1
(or k) is preferably set at a numerical value within the range that
satisfies 0.7<k.sub.1 (or k)<1.0. More preferably, parameter k.sub.1 (or
k) is within a range that satisfies 0.75.ltoreq.k.sub.1 (or k).ltoreq.0.9.
Speaking of parameter k.sub.0 (also called chroma coefficient), it is not
limited to any particular value and may appropriately be set in accordance
with the increase in the chroma of the reflection print to be reproduced
or it may be set at visually the best value; in a typical case, the
parameter k.sub.0 is preferably equal to or greater than the compression
coefficient k.sub.1, satisfying k.sub.1 .ltoreq.k.sub.0 .ltoreq.1.0. It
should also be noted that parameters k.sub.0 and k.sub.1 are in no way
limited to constants and may be varied in accordance with (B,G,R) so that
nonlinear transformation is performed as in the case of S-shaped curve
which is employed for silver halide photographic materials.
In the foregoing example, in order to accommodate the white background
D.sub.rW of a reflection medium such as a reflection print paper,
min.sub.(xy) D.sub.A which is the smallest value that can be taken by the
lightness component is used to represent the brightest point (pixel point
represented as x and y coordinates) in the image on the original
(hardcopy/softcopy image). This is not the sole case of the invention and
a constant which does not depend directly upon the lightness component
D.sub.A of the image on the original may be substituted, with the value
being selected from the range of 0.0-0.3, preferably 0.1-0.2. The specific
value of this constant depends on various factors including the
environment for exposure of the subject such as the exposure light source,
the base density of the transparent medium as the original on which the
input image is formed, the transparent medium per se and the three or more
colorants it uses, as well as on the reflection medium such as a
reflection print and the colorants it uses, which may be taken into
account as required. As already mentioned, the constant may appropriately
be selected from the range of 0.0-0.3.
In the foregoing example, the white background densities (D.sub.rW,
D.sub.rW, D.sub.rW) of the reflection medium such as a reflection print
paper are used as the base density values (signal values such as
equivalent neutral densities and integral equivalent neutral densities) of
the reflection medium with which the brightest point of the image on the
original are brought into agreement. These white background densities are
preferably signal values (BW, GW, RW) such as END and integral END which
are obtained by reading with the original image recorder such as a scanner
or CCD and subsequent transformation. The white background density
D.sub.rW of the reflection medium may be expressed by one of the thus
determined density values BW, GW and RW. Alternatively, the white
background or base density of the reflection medium may directly be
measured with a densitometer, preferably a visual densitometer, to yield a
value VW which is used to express the white background density D.sub.rW.
Described above are the basic features of the color transforming method
according to the second embodiment of the invention. In the present
invention, the subject or the image on an original is transformed to
signals, such as END or integral END, the three values of which coincide
for a plurality of colors visually perceived as gray for each pixel and
which are on a logarithmic scale with respect to the intensity of light;
the signals are then subjected to the first color transformation by the
method of the invention to perform range compression for producing color
corrected signals such as color corrected END or integral END;
subsequently, the color corrected signals are subjected to second color
transformation to produce second color transformed image data signals
which depend on the output reflection medium (e.g. reflection print) and
the colorants it uses, namely, on the printer which outputs the reflection
print. The transformation of the subject or the image on an original to
the three signals defined above, as well as the second color
transformation may be performed by any method but the use of lookup tables
is preferred.
Let us first describe the methods of constructing a lookup table LUT1 for
producing the above-defined three signals such as END or integral END, and
another lookup table LUT2 for effecting the second color transformation.
A gray scale is formed on the transparent medium such as a reversal film
which is to be used in the invention and which comprises at least three
colorants and the transmission density of the gray scale is measured at
more than one point with a scanner having three linearly independent
spectral sensitivities and a densitometer having a fourth sensitivity. The
scanner is preferably equipped with ISO narrow-band filters typically
having three peak wavelengths at 436 nm (B), 546 nm (G) and 644 nm (R) so
that it is capable of density measurement at three linearly independent
sensitivities B, G and R. The densitometer having a fourth sensitivity is
preferably a visual densitometer.
The scanner-measured transmission density is plotted on the horizontal axis
for each of B, G and R whereas the densitometer-measured transmission
density is plotted on the vertical axis for each of B, G and R, thereby
constructing the first lookup table LUT1 for transforming the original
image signals for the scanner-recorded image on the original to END or
integral END. The first lookup table LUT1 is composed of three
one-dimensional lookup tables LUT1.sub.B, LUT1.sub.G and LUT1.sub.R for B,
G and R, respectively. The scanner-measured transmission density is a
scanner-measured analytical density if the original image signals are to
be transformed to END, and it is a scanner-measured integral density in
the case of integral END.
Similarly, a gray scale is formed for the reflection medium and its
reflection density is measured with the above-described scanner and visual
densitometer; for each of B, G and R, the scanner-measured reflection
density is plotted on the vertical axis and the densitometer-measured
reflection density on the horizontal axis, thereby constructing the second
lookup table LUT2 with which the color corrected END or integral END
densities for the reflection medium are converted to the second color
transformed signals for outputting a reflection print. As in the case of
the first lookup table LUT1 , the second lookup table LUT2 is also
composed of three one-dimensional lookup tables designated LUT2.sub.B,
LUT2.sub.G and LUT2.sub.R. As in the case of the transmission density, the
scanner-measured reflection density is either a scanner-measured
analytical density (if the original image signals are to be transformed to
END) or a scanner-measured integral density (in the case of integral END).
This is how the first and second lookup tables LUT1 and LUT2 are
preliminarily constructed.
With the use of these first and second lookup tables LUT1 and LUT2, the
color transforming method of the invention is implemented in the following
manner. First, the color positive image formed on a reversal film is read
with a scanner and the obtained original image signals are transformed to
scanner-measured integral (or analytical) densities (B1,G1,R1) for each
pixel. The resulting scanner integral (or analytical) densities (B1,G1,R1)
are transformed to measured integral END (or simply END) densities
(B2,G2,R2) in accordance with the following set of equations (6) with the
intermediary of the first lookup table LUT1:
B2=LUT1.sub.B (B1)
G2=LUT1.sub.G (G1)
R2=LUT1.sub.R (R1) (6)
Subsequently, the integral END (or simply END) densities (B2,G2,R2) for
each pixel are transformed to color corrected integral END (or color
corrected END) densities (B3,G3,R3) for each pixel in accordance with the
following set of equations (5):
B3=k.sub.0 (B2-A)+k.sub.1 (A-min.sub.(xy) A)+BW
G3=k.sub.0 (G2-A)+k.sub.1 (A-min.sub.(xy) A)+GW
R3=k.sub.0 (R2-A)+k.sub.1 (A-min.sub.(xy) A)+RW (5)
The equations (5) are identical to the equations (16), except that D.sub.ri
(D.sub.rB, D.sub.rG, D.sub.rR) is replaced by (B3,G3,R3), D.sub.i
(D.sub.B, D.sub.G, D.sub.R) by (B2,G2,R2), D.sub.A by A, and D.sub.rW,
(D.sub.rW, D.sub.rW, D.sub.rW) by (BW,GW,RW).
Therefore, in equations (5), A is the lightness component specified for the
integrated END (or simply END) densities (B2,G2,R2) and it is a function
satisfying min{B2,G2,R2}.ltoreq.A.ltoreq.max{B2,G2,R2}, k.sub.0 and
k.sub.1 are constants satisfying 0<k.sub.1 <k.sub.0, (BW,GW,RW) are the
values obtained by performing inverse transform on the scanner-measured
base densities of the reflection medium by means of the second lookup
table LUT2, and min.sub.xy A of course represents the minimum value of A
for all pixels (x,y) in the entire image forming area.
In the case under consideration, the lightness component A is either OCC
(A=max{B2,G2,R2}) or UCC (A=min{B2,G2,R2}) or MCC (A=median{B2,G2,R2}).
Finally, the color corrected integral END (or color corrected END)
densities (B3,G3,R3) are transformed to integral (or analytical) densities
(B4,G4,R4) which are the second color transformed signals of the invention
in accordance with the following set of equations (7) with the
intermediary of the preliminarily constructed second lookup table LUT2 and
the integral (or analytical) densities (B4,G4,R4) are output to a printer
which then yields a reflection print:
B4=LUT2.sub.B (B3)
G4=LUT2.sub.G (G3)
R4=LUT2.sub.R (R3) (7)
provided that if the integral (or analytical) densities B4, G4 and R4 are
greater than the maximum density of said reflection medium or smaller than
its minimum density, the densities have to be clipped to said maximum or
minimum value, respectively.
The thus obtained reflection print is a reflection original which is a
faithful reproduction of the image on an original, particularly the image
on a transmission original.
The above-described color transforming method according to the second
embodiment of the invention is for creating a reflection original faithful
to the image on the original, so if the input image on the original has
the appropriate colors and densities, namely, if it is an image having
good color and density balances, the output image on the reflection
original also has the appropriate colors and densities and can be worked
up to an image having good color and density balances. In fact, however,
not all of the images on the originals delivered from users have the
appropriate colors and densities or good color and density balances. For
example, users bring in transmission positive originals such as reversal
films or transmission negative originals such as color negative films and
most of the images on these originals have the appropriate color and
density balances but one to two tenths of them are said to be upset in the
color and density balances.
Therefore, if the color transforming method of the invention is immediately
applied to such unbalanced originals, the images reproduced on the output
reflection prints will retain the upset color and density balances.
Under the circumstances, if a user has brought in an original that is upset
in color and density balances, the color transforming method of the
invention is not immediately applied; instead, in order to correct the
color and density balances of the photoelectrically read image data on the
original, setup need be performed so that the input image data on the
original are transformed to original image signals having the appropriate
balances.
On the pages that follow, we will explain the method of setting up that can
be practiced in the invention. In the embodiment under consideration, the
scanner-measured integral (or analytical) densities (B1,G1,R1) of the
input image on the original are transformed to integral END (or simply
END) densities (B2.sub.0,G2.sub.0,R2.sub.0) in accordance with the
following set of equations (8) with the intermediary of the
above-described first lookup table LUT1:
B2.sub.0 =LUT1.sub.B (B1)
G2.sub.0 =LUT1.sub.G (G1)
R2.sub.0 =LUT1.sub.R (R1) (8)
Subsequently, the integral END (or simply END) densities
(B2.sub.0,G2.sub.0,R2.sub.0) are set up by the following set of equations
(9) to determine integral END (or simply END) densities (B2,G2,R2):
B2=B2.sub.0 -BS+AS
G2=G2.sub.0 -GS+AS
R2=R2.sub.0 -RS+AS (9)
where BS, GS and RS are values that satisfy:
min.sub.(xy) B2.sub.0 .ltoreq.BS.ltoreq.max.sub.(xy) B2.sub.0
min.sub.(xy) G2.sub.0 .ltoreq.GS.ltoreq.max.sub.(xy) G2.sub.0
min.sub.(xy) R2.sub.0 .ltoreq.RS.ltoreq.max.sub.(xy) R2.sub.0
where min.sub.(xy) B2.sub.0, min.sub.(xy) G2.sub.0 and min.sub.(xy)
R2.sub.0 represent the minimum values of B2.sub.0, G2.sub.0 and R2.sub.0
for all the pixels in the entire image forming area, and max.sub.(xy)
B2.sub.0, max.sub.(xy) G2.sub.0 and max.sub.(xy) R2.sub.0 are the maximum
values of B2.sub.0, G2.sub.0 and R2.sub.0 for all the pixels in the entire
image forming area.
In equations (9), AS is a real number specified by BS, GS and RS and may be
exemplified by max{BS,GS,RS}.
The thus set up integral END (or set up END) densities (B2,G2,R2) are
subjected to the color transformation for range compression in accordance
with the procedures already described above and a reflection print is
output. The resulting reflection output reproduces an image having good
color and density balances even if it is obtained from the transmission
original which is upset in the color and density balances.
In the example just described above, the scanner-measured integral (or
analytical) densities are transformed to integral END (or simply END)
densities, which are then set up. This is not the sole case of the
invention and any other method of setting up may be employed as long as
they are capable of correcting the color and density balances in the image
signals from the original image; for example, any known methods of setting
up may be adopted, as exemplified by one which is applied to the
scanner-measured integral (or analytical) densities.
The foregoing description assumes as a representative case the system in
which the color positive image formed on the transparent medium comprising
at least three colorants is used as the image on the original, the signals
for this original image which is recorded for each pixel by means of a
scanner having three linearly independent spectral sensitivities are
transformed to scanner-measured integral densities, which are then
transformed to three-color integral END densities for use in color
transformation for range compression. This is not the sole case of the
invention and as shown in FIG. 2 (and as parenthesized in the foregoing
discussion), the invention may of course be applied to a system in which
the original image signals for a transmission positive image which is
recorded with a scanner per pixel are transformed to scanner-measured
analytical densities, which are then transformed to three-color END
densities for use in color transformation for range compression.
Other applicable systems include one in which original image signals per
pixel that are obtained by direct recording of the subject with a
solid-state imaging device such as a CCD which has three linearly
independent spectral sensitivities are used as input signals from the
original and transformed to exposure densities measured with the
solid-state imaging device, which exposure densities are then transformed
to three-color integral END densities for use in color transformation for
range compression, as well as one in which the subject is photographed on
a color negative film having three linearly independent spectral
sensitivities and transformed to exposure densities per pixel dependent on
the color negative film by means of an auxiliary scanner or solid-state
imaging device, which exposure densities are transformed to three-color
integral END densities for use in color transformation for range
compression.
The exposure densities are those integrated by the spectral sensitivities
of the imaging light-sensitive material or device for the subject; on the
other hand, they have such a property that their values coincide for a
gray subject; therefore, the exposure densities are equivalent to the
equivalent neutral densities integrated by the aforementioned spectral
sensitivities; in other words, conversion from exposure densities to
integral equivalent neutral densities is identity transformation (y=x).
In the foregoing example, the first and second lookup tables LUT1 and LUT2
are constructed and to this end, the transmission and reflection densities
of the gray scales formed on the transparent and reflection media,
respectively, are measured with the densitometer, preferably a visual
densitometer, having a fourth spectral sensitivity for B, G and R in the
scanner. This is not the sole case of the invention and it goes without
saying that the visual densitometer need not be employed and any means may
be adopted as long as they are capable of measuring the visual
transmission and reflection densities of the gray scales or concentrations
that can be regarded as equivalent to these densities. If desired, the
densitometer may be replaced by any one of B, G and R in the scanner.
In the foregoing example, in order to construct the first and second lookup
tables LUT1 and LUT2, the transmission and reflection densities of the
gray scales formed on the transparent and reflection media, respectively,
are measured actually with the scanner and the densitometer; however, this
also is not the sole case of the invention and any other means may be
employed as long as they can measure the scanner transmission and
reflection densities, as well as the visual transmission and reflection
densities obtained from the gray scales formed on the transparent and
reflection media or any densities that may be regarded as being equivalent
to these densities. There is no particular need to use the gray scales
formed on the transparent and reflection media and the densitometer can of
course be dispersed with.
In one alternative case, the first and second lookup tables LUT1 and LUT2
may be constructed in the following manner.
First, the spectral absorption waveforms of the three colorants in each of
the transparent and reflection media are measured and a spectral
absorption waveform which will produce a gray, for example, a calorimetric
gray (a*=b*=0 in the Lab space) under a light source S(.lambda.) (which
waveform is hereunder referred to as a "gray waveform") is generated for
more than one lightness value. In the next step, the generated gray
waveforms are integrated by a spectral luminous efficiency curve
V(.lambda.) and the spectral absorption waveforms of the filters in the
scanner B(.lambda.), G(.lambda.) and R(.lambda.) to construct data for
optical densities D.sub.V, D.sub.B, D.sub.G and D.sub.R. If one of the
gray waveforms is written as f(.lambda.), the optical densities D.sub.V,
D.sub.B, D.sub.G and D.sub.R, are given by the following set of equations
(10). For each of the transparent and reflection media, the optical
density D.sub.V thus obtained is plotted on the vertical axis while the
other optical densities D.sub.B, D.sub.G and D.sub.R, are plotted on the
horizontal axis, thereby constructing the first lookup table LUT1 for the
transparent medium and the second lookup table LUT2 for the reflection
medium:
##EQU12##
In the foregoing example, a colorimetric gray is used as the gray scale or
gray to construct the first and second lookup tables LUT1 and LUT2;
however, this is not the sole case of the invention and any grays may be
employed as long as they are visually perceived to be the most achromatic
(neutral). For the purposes of the invention, the calorimetric gray is not
visually the best and it is preferred to use the visually most preferred
grays which are a little shifted from the colorimetric gray (a*=b*=0) to
the negative side of the b* axis of the L*a*b* space shown in FIG. 4 and
which are within the region bounded by the dotted line; more preferably,
the grays within the region surrounded by the dashed line are used and
most preferably, the grays within the region surrounded by the solid line
should be used.
Having described the basic features of the color transforming method
according to the second embodiment of the invention, we now describe a
color transforming method according to the first embodiment of the
invention.
In the second embodiment of the invention, the input is a subject or an
image on a transmission original and the image signals to be processed by
the color transformation algorithm in the color transforming process of
the invention are signals, such as END or integral END densities, multiple
colors of which are visually perceived as gray coincide and which are on a
logarithmic scale with respect to the intensity of light. This is not the
sole case of the invention and it may be extended to signals such as TV
monitor signals multiple colors of which are visually perceived as gray
and which are on a power scale with respect to the intensity of light. It
is also possible in the invention to extend the color transformation
algorithm from the one for compressing a color space to one for
compressing and extending the color space.
Thus, in the color transforming method according to the first embodiment of
the invention, the digital image signals to be processed by an expanded
color transformation algorithm may be defined as image data represented by
signals that consist of three mutually independent elements and which,
when the values of said elements coincide, provide a color that is
visually perceived as gray.
The thus defined image data are processed with the image reproducing system
shown in FIG. 3 which includes a flow of the expanded color transformation
algorithm for the color transforming method according to the first
embodiment of the invention. The block delineated by a dashed line in FIG.
3 shows the flow color transformation algorithm for the color transforming
method according to the first embodiment of the invention. Except that the
lightness component is both compressed and extended, this is identical to
the third to fifth steps in the flow color transformation algorithm for
the color transforming method according to the second embodiment of the
invention which is shown in FIGS. 1 and 2; hence, the individual steps in
the expanded color transformation algorithm will not be described here.
As shown in FIG. 3, the color transforming method according to the first
embodiment of the invention accommodates various input images including
images on transmission originals such as color transparency originals
(e.g., reversal films and OHPs) and transparent negative originals (e.g.,
negative films), images on reflection originals such as photographic
prints and lithographic print, subjects per se, as well as images monitor
displayed on display devices such as CRTs and LCDs, and images projection
displayed as with video projectors. In short, any images can be processed
by the first embodiment of the invention as long as they can provide,
either directly or after recording or photographing or imaging (in the
latter case, either directly or through transformation), image data
represented by signals that consist of three mutually independent elements
and which, when the values of said elements coincide, provide a color that
is visually perceived as gray.
If the input image is an image on a color transparency original, a
transparent negative original or a reflection original, the same procedure
as in the second embodiment shown in FIGS. 1 and 2 is followed; the input
image is recorded with a scanner (e.g., a scanner for transmission
originals, as well as a scanner for reflection originals) or a solid-state
imaging device (e.g., CCD) and transformed to optical densities for each
pixel, which are further converted to equivalent neutral densities (END)
or integral equivalent neutral densities (integral END or IND).
Thus, in the exemplary case just mentioned above, the input image data are
represented by signals such as END or IND which consist of three mutually
independent elements and which, when the values of said elements coincide,
provide a color that is visually perceived as gray. Suppose here that the
three elements are R, G and B and that the numerical values of the
respective elements of these three image data signals coincide and are
expressed by a signal value N (B=G=R=N). Then, the signal value N is
expressed by a linear function of the logarithm of L, or the luminance of
the corresponding gray, and expressed by the following equation (2):
N=c.sub.1 logL+c.sub.2 (2)
where c.sub.1 and c.sub.2 are coefficients.
The image data signals expressed on the logarithmic scale may be any
signals of such a type that the signal value N for the gray provided when
the numerical values of all signal elements coincide is expressed by the
equation (2); specific examples include not only the END and IND mentioned
above but also exposure density, logarithmic exposure and colorimetric
density.
If the input image is a subject directly imaged with a digital camera or
video camera, or an image monitor displayed on a display device such as a
CRT or LCD or an image projection displayed on a video projector or the
like, digital image data signals B, G and R can directly be obtained.
Thus, in this exemplary case, the input image data are represented by
digital signals which consist of three mutually independent elements B, G
and R and which, when the values of said elements coincide, provide a
color that is visually perceived as gray. These input signals are such
that when the numerical values of the respective elements B, G and R
coincide and are represented by a signal value N (B=G=R=N), the signal
value N is expressed by a linear function of the power number of L, or the
luminance of the corresponding gray, and expressed by the following
equation (3):
N=c.sub.1 L.sup..gamma. +c.sub.2 (3)
where the exponent .gamma. is a real number satisfying 0<.gamma.<1 and
c.sub.1 and c.sub.2 are coefficients.
The image data signals expressed on the power scale may be any signals of
such a type that the signal value N for the gray provided when the
numerical values of all signal elements coincide is expressed by the
equation (3); specific examples include output signals from digital
cameras, video cameras and the like that can be displayed on monitors,
signals from monitors and signals from video projectors. In the case of
signals from monitors, the exponent .gamma. is selected from the range of
1/1.95 to 1/2.4 and a typical value may be 1/2.2.
If desired, the digital image data signals B, G and R to be displayed on
digital cameras, monitors and the like may be transformed to, for example,
tristimulus values X, Y and Z in the CIEXYZ color system by the following
set of equations (21) in accordance with, for example, CCIR-rec709
(Consultative Committee on International on Radio Recommendation 709) and
the resulting tristimulus values X, Y and Z are transformed by, for
example, the following set of equations (22) to yield signals N.sub.X,
N.sub.Y and N.sub.Z which are approximately expressed on a power scale;
these signals may be used as the image data to be processed by the color
transforming method in accordance with the first aspect of the invention
which are represented by signals that consist of three mutually
independent elements and which, when the values of said elements coincide,
provide a color that is visually perceived as gray:
##EQU13##
N.sub.X =(X/X.sub.0).sup.1/3
N.sub.Y =(Y/Y.sub.0).sup.1/3
N.sub.Z =(Z/Z.sub.0).sup.1/3 (22)
where X.sub.0, Y.sub.0 and Z.sub.0 are tristimulus values for the case when
R=G=B is at maximum (255).
As color management has become a common practice today, image data are
frequently given by calorimetric values such as L*,a*,b*. In this case,
N.sub.X, N.sub.Y and N.sub.Z can be determined by the following set of
equations (4) which are modifications of transformations from the CIEXYZ
color system to the CIEL*a*b* color system by the set of equations (23)
also set forth below:
L*=116(Y/Y.sub.0).sup.1/3 -16
a*=500{(X/X.sub.0).sup.1/3 -(Y/Y.sub.0).sup.1/3 }
b*=200{(Y/Y.sub.0).sup.1/3 -(Z/Z.sub.0).sup.1/3 } (23)
N.sub.X =(X/X.sub.0).sup.1/3 =(L*+16)/116+a*/500
N.sub.Y =(Y/Y.sub.0).sup.1/3 =(L*+16)/116
N.sub.Z =(Z/Z.sub.0).sup.1/3 =(L*+16)/116-b*/200 (4)
As a result of these transformations, N.sub.X, N.sub.Y and N.sub.Z provide
a calorimetric gray when their numerical values coincide and the value of
coincidence is the cube root of the luminance of the corresponding ray.
Hence, the color transforming method of the invention is readily
applicable to this case.
A word must be said about the image data signals to be processed by the
color transforming method of the invention. As already mentioned, they can
be either signals that are expressed on a logarithmic scale or those which
are expressed on a power scale. It is recognized in color science and well
known that the human sensation of lightness can be expressed either by the
logarithmic law, for example, the visual density commonly employed in
evaluation of photographs and the like, or by the power law with respect
to the luminance of the subject; in other words, the logarithmic function
and the power function have a high degree of similarity. This fact should
justify the use of the above-described two kinds of image data signals as
input for the color transformation according to the invention.
Thus, the image data signals B, G and R are obtained as input signals to be
processed by the color transforming method according to the first
embodiment of the invention (N.sub.X, N.sub.Y and N.sub.Z may be
substituted for B, G and R but in the following description, even in the
case where the use of the notation N.sub.X,N.sub.Y,N.sub.Z is appropriate,
the notation B,G,R is sometimes used if it is necessary for convenience in
explanation). Then, the color transformation algorithm delineated by the
dashed line in FIG. 3 is executed according to the first embodiment of the
invention.
First, the lightness component f(B,G,R) (=f) is determined and this is
defined between max(B,G,R) and min(B,G,R) which are the maximum and
minimum values, respectively, of the three-element image data signals B, G
and R. Subsequently, the lightness component f(B,G,R) is subtracted from
each of the three-element image data signals B, G and R to calculate the
chromaticity components of the respective elements, i.e., {B-f(B,G,R)}
(=B-f), {G-f(R,G,B)} (=G-f), and {R-f(B,G,R)} (=R-f).
In the next step, depending upon the three image data signals B, G and R,
the lightness component f is extended or compressed (namely, amplified or
attenuated) to perform dynamic range transformation (k.sub.1 f) at a
specified transformation ratio k.sub.1 (k.sub.1 >0). The ratio of dynamic
range transformation k.sub.1 (k.sub.1 >0) is determined in accordance with
the three image data signals B, G and R. If 0<k.sub.1 <1, the dynamic
range (hence, the color space) is compressed (the lightness component is
attenuated) ; on the other hand, if k.sub.1 >1, the dynamic range is
extended (the lightness component is amplified).
Subsequently, depending upon the three-element image data signals B, G and
R, the chromaticity components B-f, G-f and R-f of the three elements are
amplified or attenuated at respective specified ratios k.sub.01, k.sub.02
and k.sub.03 (k.sub.01, k.sub.02, k.sub.03 >0). This yields color
corrected chromaticity components k.sub.01 (B-f), k.sub.02 (G-f) and
k.sub.03 (R-f). The dynamic range transformed lightness component k.sub.1
f is then added to each of the color corrected chromaticity components
k.sub.01 (B-f), k.sub.02 (G-f) and k.sub.03 (R-f) to obtain color
transformed image data signals B', G' and R' (or N'.sub.X, N'.sub.Y and
N'.sub.Z). It should be mentioned that the method of color correction is
not limited to the above-described simple change in the ratio of
amplification or attenuation and other methods such as matrix operations
may be employed.
Described above is the way to obtain the image data signals that have been
color transformed by the algorithm in accordance with the first embodiment
of the invention, which may be expressed by the following set of equations
(1):
B'=K.sub.01 {B-f(B,G,R)}+k.sub.1 {f(B,G,R)-C.sub.1 }+C.sub.2
G'=K.sub.02 {G-f(B,G,R)}+k.sub.1 {f(B,G,R)-C.sub.1 }+C.sub.2
R'=K.sub.03 {R-f(B,G,R)}+k.sub.1 {f(B,G,R)-C.sub.1 }+C.sub.2(1)
where f(B,G,R) is a function that satisfies
min(B,G,R).ltoreq.f(B,G,R).ltoreq.max (B,G,R) for any set of the three
image data signals (B,G,R); the coefficients k.sub.01, k.sub.02 and
k.sub.03 and k.sub.1 are positive real numbers specified in accordance
with the three image data signals B, G and R; C.sub.1 and C.sub.2 are
constants specified by the color transforming system or the image to be
subjected to color transformation.
Typically, the coefficients k.sub.01, k.sub.02 and k.sub.03 are described
as the ratio for color correcting the chromaticity components of the
respective elements, and the lightness coefficient k.sub.1 as the ratio
for transforming the dynamic range of the lightness component. As for
C.sub.1 and C.sub.2, the stain densities of the input and output media,
respectively, may be employed.
If no specific color corrections such as the adjustment of chromaticity and
chroma or the reproduction of a preferred color are to be performed, the
coefficients of color correction k.sub.01, k.sub.02 and k.sub.03 may
assume an identical value k.sub.0 (chroma coefficient k.sub.0 >0). In this
case, the set of equations (1) may be rewritten as follows:
##EQU14##
If faithful color reproduction is to be performed using the image data
signals expressed on a logarithmic scale by the set of equations (2) or
the image data signals expressed on a power scale by the set of equations
(3), the chroma (color correction) coefficient k.sub.0 and the lightness
coefficient k.sub.1 may be set to appropriate values in accordance with
the specific color transforming system used. The following Table 1 lists
some examples of the relationship between the color transforming system
and the preferred range of each of the chroma coefficient k.sub.0 and the
lightness coefficient k.sub.1.
TABLE 1
______________________________________
Color Transforming System and Preferred Range of Chroma
Coefficient and Lightness Coefficient
Input/Output color transforming
Chroma Lightness
system coefficient k.sub.0
coefficient k.sub.1
______________________________________
Reversal film/reflective print
1.0 .ltoreq. k.sub.0 /k.sub.1 .ltoreq. 1.3
0.7 .ltoreq. k.sub.1 .ltoreq. 1.0
Negative film/reflective print
0.7 .ltoreq. k.sub.0 /k.sub.1 .ltoreq. 1.3
1.0 .ltoreq. k.sub.1 .ltoreq. 2.0
CCD camera/reflective print
0.7 .ltoreq. k.sub.0 /k.sub.1 .ltoreq. 1.3
1.0 .ltoreq. k.sub.1 .ltoreq. 2.0
Monitor/reflective print
0.7 .ltoreq. k.sub.0 /k.sub.1 .ltoreq. 1.3
1.0 .ltoreq. k.sub.1 .ltoreq. 2.0
______________________________________
The constant terms C.sub.1 and C.sub.2 in the sets of equations (1) and
(24) are input and output signal values that are correlated to each other.
Consider, for example, a negative-paper system in which a negative film is
printed on a photographic paper; with this system, it is generally held
that a gray having a reflectance of 18% is preferably finished to a gray
having a visual density of 0.75. If a print is to be obtained from a
reversal film, it is held that the brightest white in the reversal film
original is preferably finished to the brightest white on the paper.
Therefore, in the former case, C.sub.1 assumes a signal value
corresponding to the gray of 18% reflectance and C.sub.2 assumes a signal
value corresponding to the gray of 0.75 in visual density. In the latter
case, C.sub.1 assumes a signal value corresponding to the brightest white
in the reversal film original or the stain or base of the reversal
light-sensitive material whereas C.sub.2 assumes a signal value
corresponding to the white background (stain or base) of the reflection
medium (paper).
If the three image data signals which are yet to be color transformed in
the first embodiment are written as N.sub.X, N.sub.Y and N.sub.Z and the
three transformed image data signals as N'.sub.X, N'.sub.Y and N'.sub.Z,
the set of equations (24) may be rewritten as follows:
##EQU15##
As in the second embodiment, the lightness component f(B,G,R) (or
f(N.sub.X,N.sub.Y,N.sub.Z)) to be further processed in the first
embodiment may be set to have any value between max (B,G,R) (or
max(N.sub.X,N.sub.Y,N.sub.Z)) and min(B,G,R) (or
min(N.sub.X,N.sub.Y,N.sub.Z)) which are the maximum and minimum values,
respectively, of the image data signals B, G and R (or
N.sub.X,N.sub.Y,N.sub.Z). Preferably, the light component f(B,G,R) (or
f(N.sub.X,N.sub.Y,N.sub.Z)) is set to either max(B,G,R) or min(B,G,R) or
median(B,G,R) (or median(N.sub.X,N.sub.Y,N.sub.Z)), more preferably set to
median(B,G,R). Again, as in the second embodiment, the image data signals
B, G and R which are to be color transformed in the first embodiment are
preferably subjected to a setup operation so that they are transformed to
image data signals having the color and density balances corrected in the
appropriate way. As in the second embodiment, the setup operation may be
performed by any of the various methods already described above or by any
known methods.
As shown in FIG. 3, the thus obtained color transformed signals B', G' and
R' (or N'.sub.X, N'.sub.Y and N'.sub.Z) are replicated as a reproduced
image faithful to the original image such as the subject, the image on the
original or the image displayed on a monitor, either immediately or after
transformation to device-dependent data (DDD) signals. Consider, for
example the case where the output device is a printer. If the obtained
color transformed signals B', G' and R' (or N'.sub.X, N'.sub.Y and
N'.sub.Z) already have printer-dependent optical densities B', G' and R',
they are immediately input to the printer; if not, they are transformed to
printer-dependent optical densities B', G' and R', which are then input to
the printer. In either case, the printer replicates the printer-dependent
optical densities B', G' and R' on the reflection medium to yield a
reflection reproduced image (print) faithful to the original image. If the
output device is a monitor, the obtained color transformed signals B', G'
and R' (or N'.sub.X, N'.sub.Y and N'.sub.Z) are immediately input to the
monitor if they are already monitor-dependent; if not, they are
transformed to monitor-dependent signals (B',G',R'), which are then input
to the monitor. In either case, the monitor displays a replication of the
monitor-dependent signals to yield a monitor displayed reproduced image
faithful to the original image.
The original image which is to be input to the image reproducing system to
which the color transforming method according to the first embodiment of
the invention is to be applied is in no way limited to subject, color
transparency image, transparent negative image, reflection image, monitor
displayed image and the image projected on a video projector which are
described on the foregoing pages. It also goes without saying that the
reproduced image which is to be an output image is by no means limited to
the reflected image and the monitor displayed image which are described
above and, alternatively, it may be a reproduced image either replicated
on transparent media such as color transparency media (e.g. OHP paper and
reversal film) or transparent negative media (e.g. negative film) or
projected on a video projector or the like. Thus, in order to perform
color space transformation such as by dynamic range transformation and
color correction in accordance with the color transformation algorithm in
the first embodiment, the image data signals for the input/output image
defined by the input/output color space are not limited to any particular
types and may be derived from any kinds of input/output image and
input/output color space as long as they are image data represented by
signals which consist of three mutually independent elements and which,
when the values of said elements coincide, provide a color that is
visually perceived as gray or if they can be converted to such image data.
In addition, setting up or known image data processing for reproducing a
preferred color may be performed either before or after executing the
color transformation algorithm in accordance with the first embodiment of
the invention.
Described above are the basic features of the compositions of the color
transforming method according to the first embodiment of the invention and
the image reproducing system to which this method is applied.
We now describe color transforming methods according to the third and
fourth embodiments of the invention. The most characteristic feature
common to the color transforming methods according to these embodiments is
that color transformations such as dynamic range transformation and color
correction are performed using the integral equivalent neutral densities
(integral END or IND) defined in the already described second embodiment.
In the third embodiment, a color image formed on a first medium (input
medium) such as a color transparency medium, a transparent negative
medium, a reflection medium, a display medium in a monitor or a projection
medium in a video projector is replicated on a second medium (output
medium) such as a reflection medium, a display medium in a monitor, a
projection medium in a video projector or a transparent medium; to perform
the replication, the first and second media are managed by END densities
integrated by at least three independent spectral sensitivities (in other
words, the color image data on the first and second media are dealt with
as integral END data for each pixel) and the integral END densities are
used to perform the necessary processes such as color gamut transformation
(e.g. dynamic range transformation) and color correction.
Similarly, in the fourth embodiment, a subject is replicated on the various
media mentioned above, except that it is imaged with a digital camera, a
video camera or the like to be directly transformed to exposure densities
at three or more independent spectral sensitivities or, alternatively, the
subject is first photographed on a transparent medium such as a negative
or positive film and then transformed to exposure densities at three or
more independent spectral sensitivities by means of a scanner or a
solid-state imaging device; in addition, the output medium is managed with
END densities integrated by those exposure densities at three or more
independent spectral sensitivities (namely, the color image data on the
subject and the output medium are dealt with as integrated END data per
pixel) and the integrated END densities are used to perform the necessary
processes such as color gamut transformation (e.g. dynamic range
transformation) and color correction.
It should be noted that the exposure densities and integral equivalent
neutral densities to be used in the third and fourth embodiments of the
invention are not limited to the above-described image data which are
expressed on a logarithmic scale and they may be image data expressed on a
power scale (provided that the exponent .gamma. satisfies 0<.gamma.<1).
The color gamut transformation, color correction and other processes that
are performed in the third and fourth embodiments are by no means limited
to the methods for accomplishing faithful reproduction of the original
image by the color transformation algorithm for the color transforming
method according to the first and second embodiments of the invention and
any known methods of color gamut transformation, color correction and
color space transformation may be substituted. For example, the
combination of tone (or contrast) changes and matrix operations, or color
gamut transformation by three-dimensional transformation or color
correction such as the adjustment of hue or chroma or the reproduction of
a preferred color may be substituted.
According to the above-described first to fourth embodiments of the
invention, the color image formed on a subject or a first image forming
medium is replicated on a second image forming medium with the input image
data being transformed to equivalent neutral densities or expansions
thereof to integral equivalent neutral densities, followed by the
performance of appropriate lightness compression or extension at a
specified ratio, so as to output a reproduced image faithful to the input
image.
However, when the present inventor performed a visual evaluation of the
resulting reproduced image, it was found that the face should be made even
lighter whereas the blue sky should be finished "deeper" through addition
of a density.
Based on this finding, the present inventors conducted intensive studies on
the technique of selectively controlling the lightnesses of skin and sky
colors. As a result, they found that the difference between each of input
signals R, G and B and its median value A (i.e., R-A, G-A and B-A) and the
values these functions such as R-B{=(R-A)-(B-A)}, R-G, G-B take on the
ring of hues correlated to the results of the visual evaluation mentioned
above and that by performing gamma increasing and compressing or extending
the lightness component, both proper color reproduction and the selective
reproduction of the important colors in a visually preferred lightness
level could be accomplished simultaneously.
The color transforming method according to the fifth embodiment of the
invention will now be described in detail.
FIG. 5 illustrates how color transformation is performed in accordance with
the fifth embodiment of the invention. As shown, the process starts with
recording an image on a transparent negative original such as a color
negative film with a scanner so that it is input as color signals (B,G,R)
for each pixel.
The color signals (B,G,R) taken per pixel from the image on the transparent
negative original by recording with the scanner are typically digital
image data (optical densities) on the three colors R, G and B which have
been obtained by photoelectric conversion with a solid-state imaging
device such as CCD in the scanner and subsequent A/D conversion.
Alternatively, the color signals (B,G,R) may be exposure densities
transformed from the digital image data with the intermediary of the
characteristic curve (spectral sensitivities) of the transparent negative
image forming medium such as a color negative film.
In the first case of color transformation according to the fifth embodiment
of the invention, the process goes to the flow on the left side of FIG. 5
and the scanner-recorded color signals (B,G,R) are subjected, per pixel,
to the hue-dependent gamma increasing step which is the characterizing
part of the invention and which is expressed by the following equation
(26), more strictly the following equation (13), whereby gradation
hardened color signals (B',G',R') are produced:
##EQU16##
where the transforming coefficient k is a gamma increasing coefficient and
C.sub.1 and C.sub.2 are positive real numbers specified by the color
transforming system or the image to be subjected to color transformation.
The equation (13) is a combination of the equation (26) with C.sub.1 and
C.sub.2 which represents the real system more correctly. C.sub.1 and
C.sub.2 are for example stain densities of the input and output media,
respectively, and form the setup condition. In the following description
of the embodiment, the equation (26) which does not include C.sub.1 and
C.sub.2 is used for the sake of simplicity.
The gamma increasing coefficient k is a function of the color signals
(B,G,R) for each pixel. The coefficient takes a relatively small value
when the color signals (B,G,R) for each pixel take values satisfying
B>G>R, or the hue corresponding thereto is yellow red, and takes a
relatively large value when the color signals (B,G,R) for each pixel take
values satisfying B<G<R, or the hue corresponding thereto is cyan blue.
Thus, the gamma increasing coefficient k which is a transforming
coefficient, is preferably a function which includes at least one of the
differences between color signal components .DELTA.S (hereinafter referred
to as the differences between color components): (R-A), (A-B), (R-G),
(R-B) and (G-B). The function is more preferably a linear function.
The symbol A is preferably a function of the color signals for each signal
which satisfies the following equation (11) or (12):
min (B,G,R).ltoreq.A.ltoreq.max (B,G,R) (11)
min (B,R)<A<max (B,R) (12)
Especially, the symbol A represents preferably the median of the color
signals (B,G,R) for each pixel. If the median is defined as a function
representing the second largest value for a given set of (B,G,R), A can be
expressed by the following equation (27):
A=median{B,G,R} (27)
When the gamma increasing coefficient k is the linear function of one of
(R-A), (A-B), (R-G), (R-B) and (G-B), the coefficient can be expressed by
the following equation (28):
k=.alpha.+.beta..multidot..DELTA.S (28)
where .alpha. and .beta. are constants and .DELTA.S represents any one of
(R-A), (A-B), (R-G), (R-B) and (G-B) which are differences between color
components. By the use of differences between color components .DELTA.S
exemplified by (A-B) and (R-B), the equation (28) is expressed as follows:
k=.alpha.+.beta.(A-B) (28-1)
k=.alpha.+.beta.(R-B) (28-2)
By adjusting the gamma increasing coefficient k to selectively depend on
the difference between color components (R-A), (A-B), (R-G), (R-B) or
(G-B) which can be made to correspond to the hue, the important colors
such as skin color (yellow red) and blue sky (cyan blue) can be finished
in a visually preferred lightness level, namely, the skin color is
reproduced lighter and the blue sky deeper. This aspect of the invention
will now be described in greater detail.
The present inventor conducted intensive studies on the visually preferred
lightness reproduction of the important colors including the skin and sky
colors. As a result, they found that if a given set of signals (B,G,R)
result from a subtractive color mixing system (as expressed by optical
density) and if A is the median of (B,G,R), the relationships set forth in
Table 2 will hold (if the given set of signals (B,G,R) are those resulting
from an additive mixture system such as density signal of the color
negative film and monitor signal, the signs are reversed).
TABLE 2
______________________________________
Values Taken by Various Functions on Hue Ring
Coefficients
B .about.
C .about.
G .about.
Y .about.
R .about.
M
.about.
______________________________________
R-A 0 + + + 0 0 0 - - - 0
0
A-B + + 0 0 0 - - - 0 0 0 +
R-G 0 + + + + + 0 - - - - -
R-B + + + + 0 - - - - - 0 +
G-B + + 0 - - - - - 0 + + +
______________________________________
As is clear from Table 2, the difference between color signals A-B takes a
minimum value (negative) when the hue is yellow and takes a maximum value
(positive) when the hue is blue. Similarly, the difference between color
components R-A takes a maximum value (positive) when the hue is cyan and
takes a minimum value (negative) when the hue is red. Therefore, the sum
of the two functions (R-A)-(B-A)=R-B takes a minimum value (negative) when
the hue is yellow red and takes a maximum value (positive) when the hue is
cyan blue. As seen from Table 2, the same is applied not only to (A-B) and
(R-B), but also to (R-A), (R-G) and (G-B), in the sense that yellow red
(skin color) is reproduced relatively lighter and cyan blue (blue sky)
relatively deeper. Thus, considering these features, gamma increasing is
performed with the coefficient k being adjusted to depend on a difference
between color components .DELTA.S corresponding to the hue (hereinafter
expressed simply as the hue) such as (A-B), (R-B) or the like as in the
equation (28) and the appropriate color correction (to be described below)
is subsequently performed to have the important colors finished in a
visually preferred lightness level, i.e., the skin color is rendered
"relatively light" and the blue sky color "relatively deep".
For the sake of simplicity, the description below is directed to a typical
example in which the gamma increasing coefficient k (a transforming
coefficient) is a linear function of the hue (A-B) or (R-B), and A
represents the median (A=median {R,G,B}) of the color signals (R,G,B) for
each pixel, but the invention is in no way limited to this example.
In the present discussion, .alpha. is expressed as the ratio between the
contrast of the reflection print (reproduced reflection image) and the
contrast of the subject and typically takes a value of 1.8. If a
reflection print is to be prepared from the density data of a color
negative film, the value of 2.5 (.congruent.1.8/0.7) is recommended
considering the fact that the characteristic curve of the color negative
film has a gamma (.gamma.) of 0.7). However, this is not the sole case of
the invention and .alpha. may be set at any appropriate value depending
upon the input medium/input device/input color signals and the output
medium/output device/output color signals. .beta. is the parameter for
controlling the degree of gamma increasing in accordance with the hue.
The color signals (B',G',R') obtained by the hue-dependent gamma increasing
is thereafter subjected to color correction using, for example, a
3.times.3 matrix as expressed by the following equation (29), thereby
yielding color signals (B",G",R") per pixel which have been subjected to
color transformation in accordance with the invention. The transformed
color signals (B",G",R") are output per pixel to the printer.
##EQU17##
In the equation (29), (AA)={a.sub.ij, ij=1-3} represents a 3.times.3 color
correcting matrix which is used to perform color transformation from the
color space of the input system to the color space of the output system
(in the illustrated case, the color transformation is from the color space
of the image on a transparent negative original to the printer-dependent
color space). The color correcting matrix (AA) is by no means limited to
the above-mentioned 3.times.3 matrix and color correcting matrices
containing higher-order terms such as 3.times.4, 3.times.9 and 3.times.10
matrices may be substituted.
In the illustrated case, the color correcting matrix is used in the color
correction process but this is not the sole case of the invention and the
matrix may be replaced by a lookup table (hereunder abbreviated as "LUT"),
such as a three-dimensional LUT (3D-LUT). Further, in the illustrated
case, the primary colors of the output color space are R, G and B but this
is not the sole case of the invention and other sets of primary colors may
be employed, as exemplified by cyan (C), magenta (M) and yellow (Y), or
black (K) may be added to produce four colors as in printing.
The printer is thusly supplied with the color corrected color signals
(B",G",R"), which are then transformed to color signals inherent in the
printer, namely, at least three primary colors (B.sub.P,G.sub.P,R.sub.P)
for the output reflection medium inherent in the printer and on the basis
of these color signals (B.sub.P,G.sub.P,R.sub.P), a reflection print is
output which has a reflection image reproduced on an output reflection
medium such as a color paper. In the illustrated case, the color corrected
color signals (B",G",R") are fed to the printer so that they are further
transformed to printer-dependent color signals (B.sub.P,G.sub.P,R.sub.P);
however, this is not the sole case of the invention and the color
correction process may accomplish direct transformation to the
printer-dependent color signals (B.sub.P,G.sub.P,R.sub.P).
The thus obtained output reflection image is characterized by the
reproduction of the skin and blue sky colors in a visually preferred
lightness level, with the skin color finished lighter and the blue sky
deeper.
There is the second case of color transformation which is performed in
accordance with the fifth embodiment of the invention and this is shown in
the flow on the right side of FIG. 5. In this second case, the order of
gamma increasing and color correction steps is reversed and the color
correction is effected first and, thereafter, the hue-dependent gamma
increasing which is the characterizing portion of the invention is
performed. Since the only difference between the first and second cases
concerns the order of color correction and gamma increasing steps, their
details need not be given here and the following description will suffice.
Briefly, the second case of color transformation according to the fifth
embodiment of the invention starts with performing color correction on the
scanner-recorded color signals (B,G,R) as by a 3.times.3 color correcting
matrix (AA) so that they are transformed to color corrected color signals
(B.sub.a,G.sub.a,R.sub.a) [see the following equation (30)].
##EQU18##
Thereafter, as expressed by the following equation (31) or (32), the
transformed color signals (B.sub.a,G.sub.a,R.sub.a) are subjected to the
hue-dependent gamma increasing process which is the characterizing portion
of the invention using a coefficient k which is expressed by either the
following equation (33) or (34), so as to transform those signals to
(B.sub.a ',G.sub.a ',R.sub.a ') and these color transformed signals are
output to the printer:
##EQU19##
As in the first case, the color transformed signals (B.sub.a ',G.sub.a
',R.sub.a ') are transformed to printer-dependent signals
(B.sub.p,G.sub.p,R.sub.p), or signals inherent in the printer, and on the
basis of these signals (B.sub.p,G.sub.p,R.sub.p), a reproduced reflection
image is output as a reflection print. In the illustrated case, the color
signals (B.sub.a ',G.sub.a ',R.sub.a ') from the color transformation
performed in accordance with the present invention are further transformed
to the printer-dependent color signals (B.sub.p,G.sub.p,R.sub.p) in the
printer; however, this is not the sole case of the invention and the color
correction and gamma increasing processes may be so adapted that the
hue-dependent gradation hardened color signals (B.sub.a ',G.sub.a
',R.sub.a ') which are characteristic of the invention are produced direct
as the printer-dependent color signals (B.sub.P,G.sub.P,R.sub.P).
As in the first case, the reproduced reflection image thus obtained is
characterized in that the important colors such as the skin and blue
colors are reproduced in the preferred way.
In the two cases described above, explanation is facilitated by assuming
that the gamma increasing and the color correction are performed
separately on the basis of different mathematical expressions; however,
this is not the sole case of the invention and the two processes, with the
order of their performance being predetermined, may be integrated into one
routine which can be executed on the basis of a single mathematical
expression. For example, in the first case, the equation (28-1) or (28-2)
may be substituted into the equation (26), which is then substituted into
the equation (29) to reformulate the following equation (35) or (36); in
the second case, the equation (30) may be substituted into the equation
(31) or (32) to reformulate the following equation (37) or (38).
Mathematical operations for the gamma increasing and color correction may
be performed using those equations (35)-(38):
##EQU20##
In the above-described cases, the gamma increasing process is a linear
operation and provides the same result. However, the gamma increasing
process to be performed in the present invention is not theoretically
limited to a linear operation and as long as the hue-dependent gamma
increasing is performed in accordance with the invention, a nonlinear
gamma increasing process may be included prior to or after said
hue-dependent gamma increasing process. In a typical example, before or
after a nonlinear default gamma increasing process is performed, the
hue-dependent gamma increasing which is characteristic of the invention
may be performed in accordance with the following equation (39): This
method enables a nonlinear and selective gamma increasing process to be
realized in the invention.
##EQU21##
In the above-described cases, the color signals for the color space of the
input system are those taken from the image on a transparent negative
original by means of a scanner. However, this is not the sole case of the
invention and the color signals may be replaced by those taken from the
image on a color transparency original or a reflection original by means
of a scanner or those for displaying an image on the viewing screen of a
monitor. Thus, the color signals to be processed by the method of the
invention may be such that their individual elements, say, (B,G,R)
coincide in value and that the value of coincidence is given by a linear
function of the logarithm or power number of the luminance L of the
corresponding gray or, alternatively, they may be color signals on a
logarithmic scale such as optical density, exposure density, logarithmic
exposure, calorimetric density, an equivalent neutral density and integral
equivalent neutral density or they may be color signals on a power scale,
as exemplified by TV monitor signals (exponent, .gamma.=1/2.2) and
calorimetric values (exponent, .gamma.=1/3). It should be noted that these
color signals are preferably already set up as the result of adjustment in
lightness and/or white balance.
In the first and second cases of the fifth embodiment of the invention, the
gamma increasing step of the color transformation process is performed in
a hue-dependent manner such that the desired color reproduction is
accomplished with appropriate adjustment of the lightness of the important
colors in the original image, in particular, the skin and blue sky colors.
Specifically, the skin color is finished lighter than what is actually is
and the blue sky deeper. This is not the sole case of the invention and
the lightness of each color may be directly adjusted to an optimal value
in accordance with its hue, as in the color transforming method in the
third case of the fifth embodiment of the invention.
As already mentioned, the first and second embodiments of the invention are
such that the data of the original image are transformed to equivalent
neutral densities (END) or integrated extensions thereof, i.e., integral
equivalent neutral densities (integral END) and the like, and their
lightness component is subjected to appropriate compression or extension
at a specified ratio, thereby yielding a reproduced image having high
fidelity to the input image. Thus, the third case of the fifth embodiment
of the invention is a modification of the second embodiment, in which the
lightness component is compressed or extended in a hue-dependent manner so
as to ensure that the important colors, in particular, the skin and blue
sky colors are reproduced in a preferred way.
FIG. 6 is a flowchart illustrating the color transforming method according
to the third case of the fifth embodiment of the invention. The algorithm
of the flow shown in FIG. 6 is identical to the algorithm of the flow in
the second embodiment shown in FIGS. 1 and 2 except for the step of
compressing the lightness component and, hence, identical steps will not
be described in detail.
As shown, the color transforming method according to the third case of the
fifth embodiment of the invention comprises photoelectric scanner reading
of a color image photographed on a transmission original, recording the
image as original image color signals per pixel, and transforming them to
signals the three values of which coincide for a plurality of colors
visually perceived as gray for each pixel and which are on a logarithmic
scale with respect to the intensity of light, as exemplified by equivalent
neutral densities (END) or integral equivalent neutral densities
(integrated END or IND). In the following description, the transformed
signals are written as D.sub.B, D.sub.G, D.sub.R and assumed to be IND as
a representative case.
In the next step, the lightness component D.sub.A and the chromaticity
components of the respective colors .DELTA.D.sub.B, .DELTA.D.sub.G and
.DELTA.D.sub.R are calculated in accordance with the following equations
(40) and (41):
D.sub.A =median{D.sub.B,D.sub.G,D.sub.R } (40)
##EQU22##
As is clear from the equation (40), the lightness component D.sub.A is
preferably set at the median of the densities (IND) D.sub.B, D.sub.G,
D.sub.R, but may be set at any value between the maximum value and the
minimum value. The lightness component D.sub.A is set at the median to
provide a definition that makes the appearance of a specific color
compatible with its lightness.
The next step is compression of the lightness component in a hue-dependent
manner which is the most characteristic portion of the third case, in
which color corrected IND (D.sub.rB,D.sub.rG,D.sub.rR) are calculated in
accordance with the following equation (42) or (43):
##EQU23##
where k is a lightness compression coefficient which satisfies 0<k<1. In
the third case of the fifth embodiment of the invention, the lightness
compression coefficient k is defined by the following equation (44) or
(45) such that it depends on chromaticity components such as (D.sub.B
-D.sub.A) and (D.sub.R -D.sub.A):
k=.alpha.-.beta.(D.sub.B -D.sub.A)=.alpha.+.beta.(D.sub.A -D.sub.B)(44)
k=.alpha.+.beta.{(D.sub.R -D.sub.A)-(D.sub.B
-D.sub.A)}=.alpha.+.beta.(D.sub.R -D.sub.B) (45)
where .alpha. and .beta. are constants.
By thusly ensuring that the lightness compression coefficient k depends on
the chromaticity components (D.sub.B -D.sub.A) and (D.sub.R -D.sub.B)
{=(D.sub.R -D.sub.A)-(D.sub.B -D.sub.A)}, the lightness of the important
colors, in particular, the skin and blue sky colors can be compressed to a
preferred extent that is sufficiently dependent on their hues to reproduce
them as preferred colors. Stated more specifically, the skin color as such
the color of the face and the blue sky color are elicited from the hue
information and the lightness compression coefficient k for those colors
is selectively controlled such that the skin color such as the color of
the face is compressed by the greater degree to be finished lighter
whereas the blue sky color is compressed by the smaller degree to be
finished deeper and thicker. In this way, lightness compression is
achieved in a hue-dependent manner.
The above equation (43) takes into account the setup condition which
requires the brightness point in the image on the original, which is a
reversal original in the case under discussion, to coincide with the white
background D.sub.rW of the paper which is a reflection medium and
min.sub.(xy) D.sub.A in the equation (43) represents the minimal value of
D.sub.A for all pixels in the entire image forming area.
When the color corrected integrated END densities (D.sub.rB, D.sub.rG,
D.sub.rR) have been thusly computed as signals in which only the lightness
component (D.sub.A -min.sub.(xy) D.sub.A) is compressed in a hue-dependent
manner, the density signals (D.sub.rB, D.sub.rG, D.sub.rR) are converted
to output image signals (device dependent data) which are dependent on the
printer (i.e., the reflection medium used with the printer) and on the at
least three colorants formed on the reflection medium, and the printer
then yields a reproduced reflection image as a replication of the image
from the transmission original onto the reflection medium. The reproduced
image thus replicated on the reflection medium features proper or faithful
reproduction of the image from the transmission original, in which the
hues are preserved adequately or sufficiently, the highlights and shadows
are fully described and only the lightness component has been compressed
in a hue-dependent manner and the important colors, in particular the skin
color and the blue color have been reproduced in a visually preferred
lightness level.
In the invention, the description of highlights and shadows and the
reproduction of the important colors in a visually preferred lightness
level are performed positively. Hues are not completely preserved in some
cases, but are visually appropriate. The chroma is not preserved correctly
but tends to become somewhat higher than what it should be. Since the
slight increase in chroma is generally preferred from the viewpoint of
visual perception, the equation (42) should suffice for performing the
intended color transformation. However, if there is the need for chroma
adjustment, the equation (43) is preferably replaced by the following
equation (46) using not only the hue-dependent lightness compression
coefficient k.sub.1 which is the most characterizing aspect of the
invention but also a parameter k.sub.0 which satisfies 0<k.sub.1 <k.sub.0
.ltoreq.1:
D.sub.ri =k.sub.0 (D.sub.i -D.sub.A)+k.sub.1 (D.sub.A -min.sub.(xy)
D.sub.A)+D.sub.rW
D.sub.ri (x,y)=k.sub.0 {D.sub.i (x,y)-D.sub.A (x,y)}+k.sub.1 {D.sub.A
(x,y)-min.sub.(xy) D.sub.A (x,y)}+D.sub.rW (46)
where parameter k.sub.1 is the hue-dependent lightness compression
coefficient which has the same meaning as compression coefficient k
defined by the equation (44) or (45).
As to the hue-dependent lightness compression coefficient k.sub.1 (or k),
the constants .alpha. and .beta. in the above equation (44) or (45) may be
set at appropriate values that satisfy 0<k.sub.1 (k) <1.0 in accordance
with the dynamic density range of the input image on the original (e.g. a
color positive image on a reversal film) or the subject, as well the
dynamic range of the densities that can be reproduced on the output
reflection print. Considering the dynamic density range ratio for the case
where the image on a reversal original is output as a reflection print,
human vision and other factors, the lightness compression coefficient
k.sub.1 (or k) is preferably set at a value within the range that
satisfies 0.7<k.sub.1 (or k)<1.0 in a hue-dependent manner. More
preferably, the coefficient k.sub.1 (or k) is within a range that
satisfies 0.75.ltoreq.k.sub.1 (or k).ltoreq.0.9. Therefore, the constant
.alpha. of the above equations (44) and (45) is in the range which
satisfies 0<.alpha.<1.0, preferably 0.7<.alpha.<1.0, more preferably
0.75.ltoreq..alpha..ltoreq.0.9. Speaking of parameter k.sub.0 (also called
chroma coefficient), it is not limited to any particular value and may
appropriately be set in accordance with the increase in the chroma of the
reflection print to be reproduced or it may be set at visually the best
value; in a typical case, the parameter k.sub.0 is preferably equal to or
greater than the lightness compression coefficient k.sub.1, satisfying
k.sub.1 .ltoreq.k.sub.0 .ltoreq.1.0. It should also be noted that the
parameter k.sub.0 is in no way limited to the constant and may be varied
in accordance with (B,G,R) as in the hue-dependent lightness compression
coefficient k.sub.1, so that nonlinear transformation may be performed as
in the case of S-shaped curve which is employed for silver halide
photographic materials.
It should be noted that the lookup tables (see the above equations (6),
(7), (8) and (10)) and setup operation (see the equation (9) above) as
used in the second embodiment of the invention can of course be applied to
the present case. Therefore, it is needless to say that the important
colors can be reproduced in a visually preferred lightness level in the
present case, since the lightness compression coefficient k.sub.1 of the
following equation for color transformation (5) in the second embodiment
of the invention is made dependent upon the hue by the equation (47) or
(48) below.
B3=k.sub.0 (B2-A)+k.sub.1 (A-min.sub.(xy) A)+BW
G3=k.sub.0 (G2-A)+k.sub.1 (A-min.sub.(xy) A)+GW
R3=k.sub.0 (R2-A)+k.sub.1 (A-min.sub.(xy) A)+RW (5)
k.sub.1 =.alpha.+.beta.(A-B2) (47)
k.sub.1 =.alpha.+.beta.(R2-B2) (48)
where .alpha. and .beta. are constants.
A is a function which determines the lightness component as the median of
the integral END (or END) (B2, G2, R2) and which satisfies A=median
{B2,G2,R2}.
Described above are the basic features of the color transforming method
according to the third case of the fifth embodiment of the invention. We
now describe a color transforming method according to the fourth case of
the fifth embodiment of the invention.
The color transformation algorithm according to the third case can be also
extended in the fourth case of this embodiment, in the same way that the
color transformation algorithm in the color transformation processing of
the second embodiment was extended in the first embodiment of the
invention. That is, the present case also enables the extension of the
color transformation algorithm from image data signals such as END and
integral END which are on a logarithmic scale to image data signals such
as TV monitor signals which are on a power scale, and from the one for
compressing a color space to one for compressing and extending the color
space.
Thus, in the color transforming method according to the fourth case of the
fifth embodiment, the digital image data signals to be processed by an
expanded color transformation algorithm may be similarly defined as image
data represented by signals that consist of three mutually independent
elements and which, when the values of said elements coincide, provide a
color that is visually perceived as gray.
The thus defined image data are processed with the image reproducing system
shown in FIG. 7 which includes a flow of the expanded color transformation
algorithm for the color transforming method according to the fourth case
of the fifth embodiment. The image reproducing system shown in FIG. 7 is
the same as the image reproducing system shown in FIG. 3, except that the
former does not include a system for transforming the image signals of the
subject photographed with a digital camera and the image signals on the
monitor (B,G,R) to the colorimetric values (N.sub.x, N.sub.y, N.sub.z),
the lightness component f(B,G,R) of the block delineated by a dashed line
in the color transformation algorithm according to the first embodiment is
the median A (=median(B,G,R)), and that the compression or extension ratio
k.sub.1 of the lightness component A varies with the hue. The block
delineated by a dashed line in FIG. 7 shows the color transformation
algorithm which comprises a flow of the color transforming method
according to the fourth case of the fifth embodiment. Except that the
lightness component is both compressed and extended in a hue-dependent
manner, this is identical to the third to fifth steps in the color
transformation algorithm which comprises a flow of the color transforming
method according to the third case as shown in FIG. 6; hence, the
individual steps in the expanded input and output systems and the expanded
color transformation algorithm will not be described here.
Thus, when the image data signals B, G and R to be processed by the color
transforming method according to the fourth case of the fifth embodiment
of the invention are obtained in the same way as in the first embodiment,
the color transformation algorithm delineated by the dashed line in FIG. 7
is executed.
First, the lightness component A=median{B,G,R} defined as the median of the
three-element image data signals B, G and R is determined. Subsequently,
the lightness component A is subtracted from each of the three-element
image data signals B, G and R to calculate the chromaticity components of
the respective elements, i.e., (B-A), (G-A) and (R-A).
In the next step, depending upon the three image data signals B, G and R,
the lightness component A is extended or compressed (namely, amplified or
attenuated) to perform dynamic range transformation (k.sub.1 A) at a
specified hue-dependent transformation ratio k.sub.1 (k.sub.1 >0)
expressed by the equation (49) or (50) below. The ratio of hue-dependent
dynamic range transformation k.sub.1 (k.sub.1 >0) is determined in
accordance with the three image data signals B, G and R. If 0<k.sub.1 <1,
the dynamic range (hence, the color space) is compressed (the lightness
component is attenuated); on the other hand, if k.sub.1 >1, the dynamic
range is extended (the lightness component is amplified).
k.sub.1 =.alpha.+.beta.(A-B) (49)
k.sub.1 =.alpha.+.beta.(R-B) (50)
where .alpha. and .beta. are constants.
Subsequently, depending upon the three-element image data signals B, G and
R, the chromaticity components B-A, G-A and R-A of the three elements are
amplified or attenuated at respective specified ratios k.sub.01, k.sub.02
and k.sub.03 (k.sub.01, k.sub.02, k.sub.03 >0). This yields color
corrected chromaticity components k.sub.01 (B-A), k.sub.02 (G-A) and
k.sub.03 (R-A). The dynamic range transformed lightness component k.sub.1
A is then added to each of the color corrected chromaticity components
k.sub.01 (B-A), k.sub.02 (G-A) and k.sub.03 (R-A) to obtain color
transformed image data signals B', G' and R'. It should be mentioned that
the method of color correction is not limited to the above-described
simple change in the ratio of amplification or attenuation and other
methods such as matrix operations may be employed.
Described above is the way to obtain the image data signals that have been
color transformed by the color transformation algorithm according to the
fourth case, which may be expressed by the following set of equations (14)
:
B'=K.sub.01 (B-A)+k.sub.1 (A-C.sub.1)+C.sub.2
G'=K.sub.02 (G-A)+k.sub.1 (A-C.sub.1)+C.sub.2
R'=K.sub.03 (R-A)+k.sub.1 (A-C.sub.1)+C.sub.2 (14)
where k.sub.1 is the hue-dependent lightness compression coefficient
expressed by the above equation (49) or (50); A is a function which
determines the median of arbitrary three image data signals B, G and R and
which satisfies A=median{B,G,R}; the coefficients k.sub.01, k.sub.02 and
k.sub.03 are positive real numbers specified in accordance with the three
image data signals B, G and R; and C.sub.1 and C.sub.2 are constants
specified by the color transforming system or the image to be subjected to
color transformation.
Typically, the coefficients k.sub.01, k.sub.02 and k.sub.03 are described
as the ratio for color correcting the chromaticity components of the
respective elements, and the lightness coefficient k.sub.1 as the ratio
for transforming the dynamic range of the lightness component. As for
C.sub.1 and C.sub.2, the stain densities of the input and output media,
respectively, may be employed.
If no specific color corrections such as the adjustment of chromaticity and
chroma or the reproduction of a preferred color are to be performed, the
coefficients of color correction k.sub.01, k.sub.02 and k.sub.03 may
assume an identical value k.sub.0 (chroma coefficient k.sub.0 >0) . In
this case, the set of equations (14) may be rewritten as follows:
##EQU24##
If faithful color reproduction is to be performed using the image data
signals expressed on a logarithmic scale by the set of equations (2) or
the image data signals expressed on a power scale by the set of equations
(3), the chroma (color correction) coefficient k.sub.0 and the constant
term .alpha. of the lightness coefficient k.sub.1 may be set to
appropriate values in accordance with the specific color transforming
system used. The following Table 3 lists some examples of the relationship
between the color transforming system and the preferred range of each of
the chroma coefficient k.sub.0 and the constant term .alpha. of the
lightness coefficient k.sub.1.
TABLE 3
______________________________________
Color Transforming System and Preferred Range of Chroma
Coefficient and Constant Term for Lightness Coefficient
Constant term .alpha.
Input/Output color transforming
Chroma for lightness
system coefficient k.sub.0
coefficient k.sub.1
______________________________________
Reversal film/reflective print
1.0 .ltoreq. k.sub.0 /.alpha. .ltoreq. 1.3
0.7 .ltoreq. .alpha. .ltoreq. 1.0
Negative film/reflective print
0.7 .ltoreq. k.sub.0 /.alpha. .ltoreq. 1.3
1.0 .ltoreq. .alpha. .ltoreq. 2.0
CCD camera/reflective print
0.7 .ltoreq. k.sub.0 /.alpha. .ltoreq. 1.3
1.0 .ltoreq. .alpha. .ltoreq. 2.0
Monitor/reflective print
0.7 .ltoreq. k.sub.0 /.alpha. .ltoreq. 1.3
1.0 .ltoreq. .alpha. .ltoreq. 2.0
______________________________________
As shown in FIG. 7, in the same way as in the first embodiment, the thus
obtained color transformed signals B', G' and R' are sent to a printer or
a monitor, where these signals are replicated as a reproduced reflection
image (print) or a reproduced image displayed on a monitor on which the
colors of the original image such as the subject, the image on an original
or the image displayed on a monitor are properly reproduced, and of which
the important colors are reproduced in a visually preferred lightness
level.
In the color transforming method according to the fourth case of the fifth
embodiment of the invention, the image data signals are not limited to any
particular types and may be derived from any kinds of input/output image
and input/output color space. In addition, setting up or known image data
processing for reproducing a preferred color may be performed either
before or after executing the color transformation algorithm in accordance
with the present case.
Described above are the basic features of the color transforming method
according to the fourth case of the fifth embodiment of the invention and
the image reproducing system to which this method is applied.
As described above in detail, the present invention offers the following
advantages:
1) Even if the input original image is a subject, an image on a
transmission original (a transmission original hardcopy image), an image
on a reflection original (a reflection original hardcopy image) or an
image displayed as on a monitor (an original softcopy image), one can
create a reproduced hardcopy image such as a reflective print which is
extremely faithful to the input original image or, alternatively, one can
provide a monitor display of a reproduced image (a reproduced softcopy
image) which is also extremely faithful to the input original image.
2) One can create reflective prints which are extremely faithful to
subjects and transmission originals (hardcopy images) and the quality of
which is distinctively better than what is obtained by the analog system.
3) The processing system is very simple and permits realtime execution.
4) Even transmission original hardcopy images and original softcopy images
which are upset in either color balance or density balance or both can be
effectively processed to yield reproduced reflection hardcopy images or
reproduced softcopy images which feature good balances.
5) Even if the input original image is a subject, an image on a
transmission original, an image on a reflection original or an image
displayed as on a monitor, one can create a reproduced hardcopy image such
as a reflective print on which the colors of the input original image are
properly reproduced and which has the important colors, in particular the
color of the skin of the face and the blue sky color, finished in a
visually preferred lightness level to give a natural impression in a
satisfactory and highly precise manner, with the skin color rendered
relatively light and the blue sky color relatively deep or, alternatively,
one can provide a monitor display of a reproduced image (soft copy image)
on which the colors of the input original image are also properly
reproduced and which has the important colors, in particular the color of
the skin of the face and the blue sky color, finished in a visually
preferred lightness level to give a natural impression in a satisfactory
and highly precise manner, with the skin color rendered relatively light
and the blue sky color relatively deep.
6) One can create visually preferred reflective prints on which the
important colors of original images such as subjects and transmission
original hardcopy images are finished in a visually preferred lightness
level, with the skin color rendered relatively light and the blue sky
color relatively deep.
EXAMPLES
The color transforming method of the invention will now be described more
specifically with reference to the following examples.
Example 1
A reversal film [Provia 135 Format of Fuji Photo Film Co., Ltd.] was
processed with a printer [Pictrography 3000, 200 dpi (PG3000) of Fuji
Photo Film Co., Ltd.] and the input image was output on a color paper also
available from Fuji Photo Film Co., Ltd. for specific use in said printer.
A Model SG1000 (Dainippon Screen Mfg. Co., Ltd.) was used as a scanner but
the filters were replaced by ISO narrow-band filters (TCD) and the
aperture was adjusted to 25 .mu.m. The ISO narrow-band filters had the
following peak wavelengths: B at 436 nm; G at 546 nm and R at 644 nm.
In preliminary steps, a colorimetric gray scale formed on the reversal film
was measured with the scanner SG1000 and a visual densitometer (product of
X-RITE) and for each of B, G and R, the scanner-measured integral density
was plotted on the horizontal axis and the visual density on the vertical
axis to construct the first lookup table LUT1 . Similarly, a calorimetric
gray scale formed on the color paper was measured with the scanner SG1000
and the visual densitometer and for each of B, G and R, the visual density
was plotted on the horizontal axis and the scanner-measured integral
density on the vertical axis to construct the second lookup table LUT2.
Thus, a system was established for implementing the color transforming
method according to the second embodiment of the invention; see FIG. 8a ,
in which TCD.sub.int designates the scanner-measured integral density; D
the integral END of the reversal film CRT; D.sub.r the integral END of the
color paper; and PROCESS refers to the process of dynamic range (color
space) compression in accordance with the color transforming method of the
invention. The integral END depends entirely upon the spectral
sensitivities of the scanner. If the coefficient of colorimetric quality
is at unity, neither LUT1 nor LUT2 is necessary. In this sense, the
integrated END may be described as a signal obtained by gamma correction
of the scanner-measured integral density.
Thus, several frames of color transparency image were replicated to produce
a reflection print. Depending on the lightness component to be selected,
the following three algorithms were used to perform range compression:
OCC: D.sub.ri =k.sub.0 {D.sub.i (x,y)-maxD.sub.i (x,y)}+k.sub.1 {maxD.sub.i
(x,y)-min.sub.(xy) maxD.sub.i (x,y)}+D.sub.rW
MCC: D.sub.ri =k.sub.0 {D.sub.i (x,y)-medianD.sub.i (x,y)}+k.sub.1
{medianD.sub.i (x,y)-min.sub.(xy) medianD.sub.i (x,y)}+D.sub.rW
UCC: D.sub.ri =k.sub.0 {D.sub.i (x,y)-minD.sub.i (x,y)}+k.sub.1 {minD.sub.i
(x,y)-min.sub.(x,y) minD.sub.i (x,y)}+D.sub.rW (52)
The parameter k.sub.1 was optimized to ensure that the appearance of the
reflection print as perceived with the eye was the closest to that of the
reversal film. The optimization was not on a frame basis and the same
value of k.sub.1 was used for all frames. The value of parameter k.sub.0
was at unity in each algorithm but the value of parameter k.sub.1 was
varied as follows: 0.90 in OCC; 0.85 in MCC; and 0.75 in UCC. The base
densities (D.sub.rW, D.sub.rW, D.sub.rW) of the color paper were (0.1,
0.1, 0.1).
Example 2
With the same hardware configuration as used in Example 1, the image on a
reversal film was reproduced on a color paper in an output printer
(PG3000). The first and second lookup tables LUT1 and LUT2 employed in the
process were preliminarily constructed in the following manner.
For each of the reversal film and color paper, the spectral absorption
waveform was measured for each of the colorants used. Subsequently, a
spectral absorption waveform that would produce a colorimetric gray
(a*=b*=0) under a color evaluating fluorescent lamp S(.lambda.) of TOSHIBA
CORP. (which waveform is hereunder referred to as "gray waveform") was
generated for a plurality of lightness components.
The generated gray waveforms were integrated by the spectral luminance
efficiency curve V(.lambda.) and the spectral absorption waveforms of the
scanner filters B(.lambda.), G(.lambda.) and R(.lambda.) to construct data
on optical densities D.sub.V, D.sub.B, D.sub.G and D.sub.R. These
densities were determined by the set of equations (9) with one of the gray
waveforms written as f(.lambda.).
For each of the reversal film and color paper, D.sub.B, D.sub.G and D.sub.R
were plotted on the horizontal axis of a graph and D.sub.V on the vertical
axis to thereby construct a lookup table. The first lookup table
constructed for the reversal film was designated as LUT1 and the second
lookup table for the color paper as LUT2.
The signals transformed by means of the first and second lookup tables LUT1
and LUT2 were three signals within the scope of the invention the values
of which coincided for the colorimetric gray and which were on a
logarithmic scale with respect to the intensity of light.
The reversal original was recorded with a scanner and transformed to
scanner-measured densities D.sub.B, D.sub.G and D.sub.R for each pixel,
which were then transformed by means of the first lookup table LUT1.
Subsequently, three transformations UCC, MCC and OCC were performed
according to the algorithms represented by the set of equations (52). The
value of parameter k.sub.0 was at unity in each algorithm but the value of
parameter k.sub.1 was varied as follows: 0.90 in OCC; 0.85 in MCC; and
0.75 in UCC. The base densities D.sub.rW (D.sub.rW, D.sub.rW, D.sub.rW) of
the color paper were keyed to its visual density 0.1 (0.1, 0.1, 0.1).
The thus obtained values (D.sub.rB, D.sub.rG, D.sub.rR) were retransformed
to scanner-measured densities by means of the second lookup table LUT2 and
supplied to the printer PG3000 to produce a reflection print.
Example 3
With the same hardware configuration as used in Example 1, the image on a
reversal film was reproduced on a color paper in an output printer
(PG3000). The first and second lookup tables LUT1 and LUT2 employed in the
process were preliminarily constructed in the following manner.
A colorimetric gray scale formed on the reversal film was measured with the
scanner SG1000 and a visual densitometer (product of X-RITE) and for each
of B, G and R, the scanner-measured analytical density was plotted on the
horizontal axis and the visual density on the vertical axis to construct
the first lookup table LUT1. Similarly, a calorimetric gray scale formed
on the color paper was measured with the scanner SG1000 and the visual
densitometer and for each of B, G and R, the visual density was plotted on
the horizontal axis and the scanner-measured analytical density on the
vertical axis to construct the second lookup table LUT2.
Thus, a system was established for implementing the color transforming
method according to the second embodiment of the invention; see FIG. 8b,
in which TCD.sub.ana designates the scanner-measured analytical density; D
the END of the reversal film; D.sub.r the END of the color paper; and
PROCESS refers to the process of dynamic range (color space) compression
in accordance with the color transforming method of the invention. The END
is a concept introduced by Evans and refers to a technique by which the
value of the visual density of a gray equivalent to a given set of
colorants is assigned to the colorants of interest. Since END is a value
inherent in a specific colorant, it is not dependent on the spectral
sensitivities of the scanner.
Thus, several frames of color transparency image were replicated to produce
a reflection print.
For the selection of the lightness components in the algorithms for range
compression, the values of parameters k.sub.0 and k.sub.1 and the base
density of the color paper, see the relevant description in Example 1.
The reflection prints obtained in Examples 1, 2 and 3 were examined
visually and evaluated. As general characters, all prints were extremely
faithful to the images on the reversal film originals (hereunder referred
to as "reversal originals") and the colors characteristic of the reversal
originals were solidly reproduced. In addition, all prints were higher in
chroma than their originals. Since the reflection prints were extremely
faithful to the reversal originals, the characters of the latter were
reflected in the former most faithfully (i.e., they even reflected the
problems with the reversal originals in that they were superb with nature
photos but showed a tendency to produce a skin color of too high densities
in portraits) . Further, the prints were partially "color-blind" in
brilliant colors as in flowers. Plausible causes of this phenomenon
include the non-linear correlationship between density and visual
perception (i.e., Weber-Fechner's law does not hold strictly) and the
inability of hues to be defined by the ratio of antialgorithms. Whichever
the true reason, the high-chromaticity (color blindness) problem can be
alleviated by changing the value of parameter k.sub.0. The high chroma is
a problem to the purpose of achieving faithful reproduction but if the
final product is intended for ordinary users, this is more preferred than
disliked and may well be described as a desirable result.
The following are the results of evaluation according to the selection of
different lightness components. In OCC, the contrast was so high (compared
to the original) that the brightness of the face was compatible with the
solidness of black. In addition, the clearness of white was satisfactory
(better than the original). However, the degree of color blindness was
highly noticeable. In MCC, the print featured very high fidelity to the
original. In UCC, the brightness of the skin color and the solidness of
black were tradeoffs. The contrast was low. On the other hand, best
results were attained in the problem of color blindness.
Each of the three transformation formulae for OCC, MCC and UCC yielded a
print the impression of which was very close to that of the image on the
input original (reversal film). It had the high level of fidelity so far
unattainable by the prior art. Further, the method of the invention was so
convenient that it was quite outstanding in the computing speed and
operating cost.
Thus, the effectiveness of the color transforming method according to the
second embodiment of the invention is obvious.
In terms of fidelity to the original, MCC is the best but considering the
color quality of the print per se, OCC would be better. This could derive
from the difference in viewing conditions between the image on the
reversal film and the image on the reflection print.
In the system shown in FIG. 8a, the integral END densities used in Examples
1 and 2 depend entirely upon the spectral sensitivities of the scanner;
however, in the system shown in FIG. 8b, the END densities used in Example
3 are inherent in the colorants and, hence, do not depend on the spectral
sensitivities of the scanner. The END is an analytical density, so if the
difference in colorants between the images on a transmission and a
reflection original is not considered, the hues of certain colors, for
example, magentas can potentially have offsets. In addition, the END does
not take into account the fact that compared to the reversal film which is
viewed under transmitted light, the color paper which is viewed under
reflected light suffers from a comparatively great increase in unwanted
absorption. However, if the difference in colorants between the images on
the transmission and reflection originals is not a problem or is fully
taken into account, an END using system such as the one established in
Example 3 can reproduce an image on a reflection print which is highly
faithful to the image on the transmission original.
Example 4
The image data on an appropriately exposed color reversal film (Fuji Chrome
Provia of Fuji Photo Film Co., Ltd.) was recorded with a drum scanner
(SG1000 of Dainippon Screen Mfg. Co., Ltd.) as in Example 3 and
transformed to optical densities per pixel, which in turn were transformed
to equivalent neutral densities (END). The resulting image data was
subjected to the following transformation:
##EQU25##
where k.sub.0 =1.0 and k.sub.1 =0.9; the constants 0.16 and 0.1 refer to
the stain densities of the color reversal film and the color photographic
paper, respectively.
As in Example 3, the transformed image data were processed with an END
managed color printer (Pictrography (PG) 3000 of Fuji Photo Film Co.,
Ltd.), thereby outputting a reflection print that was extremely faithful
to the color reversal film.
Example 5
A subject was imaged with a digital steel camera (DS300 of Fuji Photo Film
Co., Ltd.) and the obtained image data were subjected to the following
transformation:
##EQU26##
where k.sub.0 =1.1 and k.sub.1 =0.9. Any signal value that was less than 0
or greater than 255 was clipped to 0 or 255, respectively.
The transformed image data were displayed on a PC monitor (Multiscan17seII
of SONY CORP.) The resulting monitor image was faithful to the subject.
Example 6
Image data displayed on a PC monitor (Multiscan17seII) were subjected to
the following transformation:
##EQU27##
where k.sub.1= 1.7 and k.sub.2 =1.5. Any signal value that was less than 0
or greater than 255 was clipped to 0 or 255, respectively.
The transformed image data were output with a color printer (Pictrography
3000) to yield a reflection print faithful to the monitor image.
Example 7
Image data displayed on a PC monitor (Multiscan17seII) was transformed to
tristimulus values X, Y and Z in accordance with CCIR-rec709 and the
obtained tristimulus values X, Y and Z were subjected to the following
transformation:
##EQU28##
where X.sub.0, Y.sub.0 and Z.sub.0 are tristimulus values for the case
when B=G=R=255. The obtained image data were subjected to the following
transformation:
##EQU29##
where k.sub.1 =1.7 and k.sub.2 =1.5. Any signal value that was greater
than 1.0 or less than 0.0 was clipped to 1.0 or 0.0, respectively.
The transformed image data were further transformed to calorimetric values
which were output to a color printer (Pictrography 3000) managed with
calorimetric values in which the white background of the photographic
paper was a reference white. As a result, there was yielded a reflection
print faithful to the monitor image.
Example 8
A color negative film (SG400 of Fuji Photo Film Co., Ltd.) was
preliminarily exposed in tones under white light. After development, the
image density was measured with a drum scanner (SG1000 of Dainippon Screen
Mfg. Co., Ltd.) and the scanner-measured integral density was plotted on
the horizontal axis and the exposure density on the vertical axis to
construct the first lookup table.
In a separate step, a color paper for specific use on Pictrography 3000
(printer of Fuji Photo Film Co., Ltd.) was processed to generate
colorimetric gray waveforms as in Example 2, which were integrated with
the spectral sensitivities or spectral luminous efficiency curves of a
color negative film (SG400) to calculate optical density data. The
spectral sensitivity integrated density was plotted on the vertical axis
and the visual density on the horizontal axis to construct the second
lookup table.
A subject was photographed on a color negative film (SG400), after
development, the image data were recorded with a scanner (SG1000) and
transformed to integral densities per pixel, which in turn were
transformed to exposure densities with the intermediary of the first
lookup table, followed by the following arithmetic operation:
##EQU30##
where N is a gray's exposure density providing a reflectance of 18%.
Subsequently, the densities (B',G',R') were transformed to spectral
sensitivity integrated densities with the intermediary of the second
lookup table; the integral densities were output by means of Pictrography
3000 to yield a print extremely faithful to the subject.
In this example, the chroma coefficient k.sub.0 was relatively smaller than
the lightness coefficient k.sub.1 because the color negative film used
(SG400) featured great chemical chroma enhancement (i.e., interlayer
effect). Therefore, if a color negative film having only a weak interlayer
effect is to be used or in the case where the transformation from the
scanner-measured integral density to the exposure density is accompanied
by a procedure of eliminating the interlayer effect, the chroma
coefficient k.sub.0 preferably assumes a little greater value.
Example 9
In Examples 1-4, the image data on the reversal originals were transformed
to equivalent neutral densities or integral equivalent neutral densities
(B,G,R) per pixel, which were then subjected to the following
transformation:
B'=1.0-10.sup.-(B-0.16)/3
G'=1.0-10.sup.-(G-0.16)/3
R'=1.0-10.sup.-(R-0.16)/3
Thereafter, the following color transformation was effected:
##EQU31##
Subsequently, the following transformation was performed:
B'=-3 log.sub.10 (1-B)+0.1
G'=-3 log.sub.10 (1-G)+0.1
R'=-3 log.sub.10 (1-G)+0.1
The transformed signals were further transformed to analytical or integral
densities with the intermediary of the second lookup table and output by
means of Pictrography 3000 to yield prints extremely faithful to the
reversal originals. As can be seen from this example, the effectiveness of
the invention is fully retained even if the equivalent neutral densities
or integral equivalent neutral densities are represented on a cube root
scale rather than on a logarithmic scale.
Example 10
A subject was photographed on SG400 (color negative film of Fuji Photo Film
Co., Ltd.) and output to a printer as in Example 8, except that the
scanner and the printer were changed from SG1000 and Pictrography 3000 to
Digital Lab System Frontier of Fuji Photo Film Co., Ltd. (the combination
of high-speed scanner/image processing workstation SP-1000 and laser
printer/paper processor LP-1000P). As a result, there was yielded a print
which was extremely faithful to the subject.
As is clear from Examples 4-10, the image reproduced on the reflection
print, as well as the image reproducing the display on the monitor which
were obtained by applying the color transforming method according to the
first embodiment of the invention were a faithful reproduction of the
input original image irrespective of whether it was the image on a
transmission original such as a reversal film, or a subject or an image
displayed on a monitor.
Therefore, the effectiveness of the color transforming method according to
the first embodiment of the invention is obvious.
It should also be noted that the effectiveness of the color transforming
method according to the third embodiment of the invention is obvious from
Examples 1-10 and it is also obvious that the same effectiveness can be
achieved by the color transforming method according to the fourth
embodiment of the invention.
Example 11
An exposed and developed color negative film (Super G ACE400 of Fuji Photo
Film Co., Ltd.) was read with a scanner (Frontier of Fuji Photo Film Co.,
Ltd.) and the input image data were transformed to color signals (B,G,R)
for each pixel. Then, the following four kinds of mathematical operations
for hue-dependent gamma increasing were performed:
##EQU32##
were "median" represents the median value of said color signals (B,G,R)
for each pixel.
The thus transformed color signals (B',G',R') were subjected to color
correction through the image processing circuit packaged in a digital
color printer (Frontier of Fuji Photo Film Co., Ltd.), from which the
color corrected signals were output to yield in all cases visually
preferred reflection prints.
Example 12
An exposed and developed color reversal film (Provia of Fuji Photo Film
Co., Ltd.) was read with a drum scanner (SG1000 of Dainippon Screen Mfg.
Co., Ltd.) and the color signals for each pixel were transformed to
equivalent neutral densities (B,G,R) for each pixel. Then, the following
two kinds of mathematical operations for hue-dependent gamma increasing
were performed:
##EQU33##
where "max" represents the maximum value of the color signals (B,G,R) for
each pixel.
The thus obtained equivalent neutral densities (B',G',R') were transformed
to QL values of a color printer (Pictrography 3000 of Fuji Photo Film Co.,
Ltd.), with the intermediary of a tridimensional lookup table which
represents the relationship between the equivalent neutral densities for a
color image formed on a photographic paper exclusively used in the color
printer and the QL values (0 to 255) of the color printer corresponding to
the color image formed. The obtained QL values were output from the color
printer to yield in both cases visually preferred reflection prints.
Example 13
A subject was imaged with a digital steel camera (DS300 of Fuji Photo Film
Co., Ltd.) and the obtained image data were transformed to color signals
(B,G,R) for each pixel, which were then subjected to the following
mathematical operation:
##EQU34##
where "min" represents the minimum value of the color signals (B,G,R) for
each pixel.
The thus obtained color signals (B', G', R') were displayed on a PC monitor
(Multiscan17seII of SONY CORP.). A visually preferred monitor image was
obtained. cl Example 14
A subject was imaged with a digital steel camera (DS300 of Fuji Photo Film
Co., Ltd.) and the obtained image data were transformed to color signals
(B, G, R) for each pixel, which were then subjected to the following
mathematical operation:
##EQU35##
where "min" represents the minimum value of the color signals (B,G,R) for
each pixel.
The thus obtained color signals (B', G',R') were displayed on a color
printer (Pictrography 3000 of Fuji Photo Film Co., Ltd.). A visually
preferred print image was obtained.
As is clear from Examples 11 to 14, reproduced images such as the
reflection print and the monitor-displayed image obtained by the color
transforming method according to the fifth embodiment of the invention
were those on which the colors of an input original image were properly or
faithfully reproduced, with the important colors, that is, the color of
the skin of the face and the blue sky color being reproduced in a visually
preferred lightness level, and which give a natural impression in a
satisfactory manner, irrespective of the nature of the input original
image. Therefore, the effect of the color transforming method according to
the fifth embodiment of the invention is apparent.
While the basic features of the color transforming methods according to the
four embodiments of the invention have been described above, it should be
noted that these are not the sole cases of the invention and various
improvements and design modifications may be made without departing from
the scope and spirit of the invention.
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